Details

Time bar (total: 2.7s)

analyze5.0ms (0.2%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%75%0%0%25%0%3
40%25%37.5%0%0%37.5%0%4
66.7%37.5%18.7%0%0%43.7%0%5
82.4%43.7%9.4%0%0%46.9%0%6
90.9%46.9%4.7%0%0%48.4%0%7
95.4%48.4%2.3%0%0%49.2%0%8
97.7%49.2%1.2%0%0%49.6%0%9
98.8%49.6%0.6%0%0%49.8%0%10
99.4%49.8%0.3%0%0%49.9%0%11
99.7%49.9%0.1%0%0%49.9%0%12
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.1s (40.4%)

Results
1.1s8256×body256valid
1.0ms14×body256invalid
Bogosity

preprocess147.0ms (5.5%)

Algorithm
egg-herbie
Rules
994×rational_best_oopsla_all_46_json_45_simplify-35
838×rational_best_oopsla_all_46_json_45_simplify-89
816×rational_best_oopsla_all_46_json_45_simplify-108
740×rational_best_oopsla_all_46_json_45_simplify-74
612×rational_best_oopsla_all_46_json_45_simplify-72
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01233
11833
23033
36333
422033
5116533
6408333
7683733
011
Stop Event
saturated
node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify140.0ms (5.2%)

Algorithm
egg-herbie
Rules
994×rational_best_oopsla_all_46_json_45_simplify-35
838×rational_best_oopsla_all_46_json_45_simplify-89
816×rational_best_oopsla_all_46_json_45_simplify-108
740×rational_best_oopsla_all_46_json_45_simplify-74
612×rational_best_oopsla_all_46_json_45_simplify-72
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01233
11833
23033
36333
422033
5116533
6408333
7683733
Stop Event
node limit
Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

eval0.0ms (0%)

Compiler

Compiled 12 to 10 computations (16.7% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Compiler

Compiled 12 to 10 computations (16.7% saved)

localize18.0ms (0.7%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))
Compiler

Compiled 45 to 34 computations (24.4% saved)

series2.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0ms
x
@inf
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0ms
x
@inf
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0ms
x
@0
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0ms
x
@-inf
(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite82.0ms (3%)

Algorithm
batch-egg-rewrite
Rules
1480×rational_best_oopsla_all_46_json_45_simplify-13
1414×rational_best_oopsla_all_46_json_45_simplify-23
964×rational_best_oopsla_all_46_json-2
964×rational_best_oopsla_all_46_json-1
964×rational_best_oopsla_all_46_json-4
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01069
15269
211469
338769
4178769
Stop Event
node limit
Counts
3 → 140
Calls
Call 1
Inputs
(/.f64 (-.f64 1 x) (+.f64 1 x))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
Outputs
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simplify132.0ms (4.9%)

Algorithm
egg-herbie
Rules
1348×rational_best_oopsla_all_46_json_45_simplify-23
1042×rational_best_oopsla_all_46_json_45_simplify-89
890×rational_best_oopsla_all_46_json_45_simplify-35
886×rational_best_oopsla_all_46_json_45_simplify-24
858×rational_best_oopsla_all_46_json_45_simplify-74
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03434404
113024362
261564362
Stop Event
node limit
Counts
168 → 189
Calls
Call 1
Inputs
1
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-1
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-1
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1
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(/.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (/.f64 (*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (/.f64 1 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (/.f64 1 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))))
(neg.f64 (neg.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
Outputs
1
(+.f64 1 (*.f64 -2 x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 1 (*.f64 -2 x)))
(+.f64 1 (+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 x)))
(+.f64 1 (+.f64 (*.f64 -2 x) (*.f64 2 (pow.f64 x 2))))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 -2 x) (*.f64 -2 (pow.f64 x 3)))))
(+.f64 1 (+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 -2 x) (*.f64 -2 (pow.f64 x 3)))))
(+.f64 (*.f64 -2 (+.f64 x (pow.f64 x 3))) (+.f64 (*.f64 2 (pow.f64 x 2)) 1))
(+.f64 (*.f64 -2 (+.f64 x (pow.f64 x 3))) (+.f64 1 (*.f64 2 (pow.f64 x 2))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(+.f64 (*.f64 2 (/.f64 1 x)) -1)
(+.f64 -1 (*.f64 2 (/.f64 1 x)))
(-.f64 (*.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 -1 (-.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))
(-.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (*.f64 2 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 -1 (-.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(+.f64 (*.f64 2 (/.f64 1 x)) -1)
(+.f64 -1 (*.f64 2 (/.f64 1 x)))
(-.f64 (*.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 -1 (-.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))
(-.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (*.f64 2 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 -1 (-.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (*.f64 x -1))
(+.f64 1 (neg.f64 x))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 (*.f64 (pow.f64 x 2) 1/2) (+.f64 1 (*.f64 x -1)))
(+.f64 (+.f64 1 (neg.f64 x)) (*.f64 (pow.f64 x 2) 1/2))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(+.f64 (*.f64 (pow.f64 x 3) -1/2) (+.f64 (*.f64 (pow.f64 x 2) 1/2) (+.f64 1 (*.f64 x -1))))
(+.f64 (*.f64 (pow.f64 x 2) 1/2) (+.f64 1 (+.f64 (neg.f64 x) (*.f64 (pow.f64 x 3) -1/2))))
(sqrt.f64 -1)
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (-.f64 2 (*.f64 -1 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))))
(+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (+.f64 (*.f64 1/2 (/.f64 (-.f64 2 (*.f64 -1 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 (pow.f64 x 3) (sqrt.f64 -1)))) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1)))))))
(+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (-.f64 2 (neg.f64 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 (pow.f64 x 3) (sqrt.f64 -1)))) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1)))))))
(sqrt.f64 -1)
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1)))))
(+.f64 (+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1)))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (*.f64 1/2 (/.f64 (+.f64 2 (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))))
(+.f64 (*.f64 1/2 (/.f64 (+.f64 2 (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (*.f64 (pow.f64 x 3) (sqrt.f64 -1)))) (+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1)))))))
(+.f64 (+.f64 (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1))))) (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (*.f64 (pow.f64 x 3) (sqrt.f64 -1)))))
(+.f64 (+.f64 (+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1)))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (pow.f64 x 2) (sqrt.f64 -1))))) (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (*.f64 (pow.f64 x 3) (sqrt.f64 -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 -1 x)) (-.f64 1 (*.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 x -1)) (-.f64 1 (*.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 -1 x)) (-.f64 1 (*.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 x -1)) (-.f64 1 (*.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 -1 x)) (-.f64 1 (*.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 x -1)) (-.f64 1 (*.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 -1 x)) (-.f64 1 (*.f64 -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 x -1)) (-.f64 1 (*.f64 x -1)))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(+.f64 0 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (*.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 (-.f64 1 x) (+.f64 1 x))) (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 (-.f64 1 x) (+.f64 1 x)))) 0))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (*.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 0))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 0 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (*.f64 (neg.f64 (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 (-.f64 1 x) (+.f64 1 x)))) 0))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(-.f64 0 (neg.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(-.f64 (*.f64 0 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x))))) (*.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (neg.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(-.f64 (*.f64 0 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 (-.f64 1 x) (+.f64 1 x))) (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 (-.f64 1 x) (+.f64 1 x))))) (*.f64 (*.f64 (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 (-.f64 1 x) (+.f64 1 x))) (/.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) (/.f64 (-.f64 1 x) (+.f64 1 x)))) (neg.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(/.f64 (-.f64 1 x) (+.f64 1 x))
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(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
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(*.f64 (neg.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) -1)
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eval109.0ms (4.1%)

Compiler

Compiled 6741 to 5507 computations (18.3% saved)

prune23.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1872189
Fresh000
Picked011
Done000
Total1873190
Error
0.0b
Counts
190 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
0.8b
(*.f64 2 (atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))))
1.0b
(*.f64 2 (atan.f64 (+.f64 1 (neg.f64 x))))
0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Compiler

Compiled 35 to 30 computations (14.3% saved)

localize9.0ms (0.3%)

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize24.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 x 2)
0.0b
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
0.0b
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
0.0b
(*.f64 1/2 (pow.f64 x 2))
Compiler

Compiled 63 to 51 computations (19% saved)

series2.0ms (0.1%)

Counts
4 → 10
Calls

12 calls:

TimeVariablePointExpression
0.0ms
x
@0
(*.f64 1/2 (pow.f64 x 2))
0.0ms
x
@-inf
(pow.f64 x 2)
0.0ms
x
@inf
(pow.f64 x 2)
0.0ms
x
@inf
(*.f64 1/2 (pow.f64 x 2))
0.0ms
x
@inf
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))

rewrite133.0ms (4.9%)

Algorithm
batch-egg-rewrite
Rules
1246×rational_best_oopsla_all_46_json-2
1246×rational_best_oopsla_all_46_json-1
1246×rational_best_oopsla_all_46_json-4
1246×rational_best_oopsla_all_46_json-3
864×rational_best_oopsla_all_46_json_45_simplify-72
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01486
17982
216882
352674
4243174
5763374
Stop Event
node limit
Counts
4 → 177
Calls
Call 1
Inputs
(*.f64 1/2 (pow.f64 x 2))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(pow.f64 x 2)
Outputs
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simplify150.0ms (5.6%)

Algorithm
egg-herbie
Rules
1634×rational_best_oopsla_all_46_json_45_simplify-23
1178×rational_best_oopsla_all_46_json_45_simplify-89
984×rational_best_oopsla_all_46_json_45_simplify-24
932×rational_best_oopsla_all_46_json_45_simplify-74
718×rational_best_oopsla_all_46_json_45_simplify-13
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03444261
112943955
274143955
Stop Event
node limit
Counts
187 → 199
Calls
Call 1
Inputs
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
1
(+.f64 1 (*.f64 -1 x))
(*.f64 1/2 (pow.f64 x 2))
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(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))
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(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 0 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
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(*.f64 (pow.f64 x 2) (*.f64 1 (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (/.f64 1/2 (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 (pow.f64 x 2) (/.f64 1/2 (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))))))
(*.f64 (pow.f64 x 2) (*.f64 (pow.f64 x 2) (/.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2))))
(*.f64 (pow.f64 x 2) (*.f64 (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2))) (/.f64 (pow.f64 x 2) (pow.f64 x 2))))
(*.f64 (pow.f64 x 2) (*.f64 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (/.f64 (pow.f64 x 2) (pow.f64 x 2))))
(*.f64 (pow.f64 x 2) (*.f64 (pow.f64 x 2) (/.f64 (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2))) (pow.f64 x 2))))
(*.f64 (pow.f64 x 2) (*.f64 (pow.f64 x 2) (/.f64 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (pow.f64 x 2))))
(*.f64 (pow.f64 x 2) (-.f64 1/2 (*.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (-.f64 1/2 (*.f64 -1/2 (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2))))))
(*.f64 (pow.f64 x 2) (-.f64 1/2 (*.f64 -1/2 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))))))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) -1/2))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 -1/2 (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2))))))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 -1/2 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))))))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 (pow.f64 x 2) (/.f64 1/2 (pow.f64 x 2))) -1/2))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 (pow.f64 x 2) (/.f64 1/2 (pow.f64 x 2))) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 (pow.f64 x 2) (/.f64 1/2 (pow.f64 x 2))) (*.f64 -1/2 (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2))))))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 (pow.f64 x 2) (/.f64 1/2 (pow.f64 x 2))) (*.f64 -1/2 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))))))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))) -1/2))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))) (*.f64 -1/2 (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2))))))
(*.f64 (pow.f64 x 2) (-.f64 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))) (*.f64 -1/2 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))))))
(*.f64 (*.f64 1/2 (pow.f64 x 2)) 2)
(*.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 1 (/.f64 (pow.f64 x 2) (pow.f64 x 2))))
(*.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 1 (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2)))))
(*.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 1 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))))
(*.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2)))))
(*.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 1 (pow.f64 x 2))
(*.f64 1 (*.f64 (*.f64 (pow.f64 x 2) 2) 1/2))
(*.f64 -1 (neg.f64 (pow.f64 x 2)))
(*.f64 -1 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (neg.f64 (pow.f64 x 2))))
(*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2))
(*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 (pow.f64 x 2) (/.f64 1 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 (pow.f64 x 2) (/.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 (neg.f64 (pow.f64 x 2)) (/.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 (pow.f64 x 2) (/.f64 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (*.f64 (neg.f64 (pow.f64 x 2)) (/.f64 (neg.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 -1/2 (-.f64 (neg.f64 (pow.f64 x 2)) (pow.f64 x 2)))
(*.f64 (neg.f64 (pow.f64 x 2)) -1)
(*.f64 (neg.f64 (pow.f64 x 2)) (neg.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2))))
(*.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 (pow.f64 x 2) 2))
(*.f64 (*.f64 (pow.f64 x 2) (/.f64 1 (pow.f64 x 2))) (pow.f64 x 2))
(*.f64 (*.f64 (pow.f64 x 2) -1/2) -2)
(*.f64 (*.f64 (pow.f64 x 2) -1/2) (-.f64 (neg.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) 1))
(*.f64 (*.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (pow.f64 x 2))
(*.f64 (neg.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (neg.f64 (pow.f64 x 2)))
(/.f64 (pow.f64 x 2) 1)
(/.f64 (pow.f64 x 2) (/.f64 (pow.f64 x 2) (pow.f64 x 2)))
(/.f64 (pow.f64 x 2) (/.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))))
(neg.f64 (neg.f64 (pow.f64 x 2)))
Outputs
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (neg.f64 x))
(-.f64 1 x)
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x))
(-.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x))
(-.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) 0)
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 0 (/.f64 (pow.f64 x 2) (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 0 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 0 (*.f64 1/2 (pow.f64 x 2)))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 0 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 1/2 (pow.f64 x 2)))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 0 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))) (*.f64 1/2 (pow.f64 x 2)))
(*.f64 1/2 (pow.f64 x 2))
(-.f64 (*.f64 1/2 (pow.f64 x 2)) 0)
(*.f64 1/2 (pow.f64 x 2))
(-.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 (*.f64 0 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 1/2 (pow.f64 x 2))
(-.f64 0 (*.f64 (pow.f64 x 2) -1/2))
(neg.f64 (*.f64 (pow.f64 x 2) -1/2))
(-.f64 (*.f64 0 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 (pow.f64 x 2) -1/2))
(neg.f64 (*.f64 (pow.f64 x 2) -1/2))
(-.f64 (+.f64 0 (*.f64 0 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))) (*.f64 (pow.f64 x 2) -1/2))
(neg.f64 (*.f64 (pow.f64 x 2) -1/2))
(-.f64 (+.f64 (*.f64 0 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 0 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))) (*.f64 (pow.f64 x 2) -1/2))
(neg.f64 (*.f64 (pow.f64 x 2) -1/2))
(-.f64 (+.f64 0 (*.f64 0 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))))) (*.f64 (pow.f64 x 2) -1/2))
(neg.f64 (*.f64 (pow.f64 x 2) -1/2))
(-.f64 (+.f64 (*.f64 0 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 0 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))))) (*.f64 (pow.f64 x 2) -1/2))
(neg.f64 (*.f64 (pow.f64 x 2) -1/2))
(/.f64 (*.f64 1/2 (pow.f64 x 2)) 1)
(*.f64 1/2 (pow.f64 x 2))
(/.f64 (*.f64 1/2 (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2)))
(*.f64 1/2 (pow.f64 x 2))
(/.f64 (*.f64 1/2 (pow.f64 x 2)) (/.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(/.f64 (*.f64 1/2 (pow.f64 x 2)) (/.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 x 2)))))
(*.f64 1/2 (pow.f64 x 2))
(/.f64 (*.f64 (pow.f64 x 2) -1/2) -1)
(neg.f64 (*.f64 (pow.f64 x 2) -1/2))
(neg.f64 (*.f64 (pow.f64 x 2) -1/2))
(+.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) 0)
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(+.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (*.f64 0 (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(+.f64 0 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(+.f64 (*.f64 0 (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(-.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) 0)
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(-.f64 0 (neg.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(-.f64 (+.f64 0 (*.f64 0 (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))))) (neg.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 1 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 -1 (neg.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 -1 (*.f64 1 (neg.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 -1 (*.f64 (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))) (neg.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) 1)
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (*.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (/.f64 1 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (*.f64 (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))) (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (*.f64 1 (*.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (/.f64 1 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (*.f64 (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))) (*.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (/.f64 1 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
(*.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (*.f64 (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))) (*.f64 (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))) (/.f64 (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2))) (atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))))))
(atan.f64 (-.f64 (-.f64 1 x) (*.f64 (pow.f64 x 2) -1/2)))
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(*.f64 (neg.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2))) (neg.f64 (pow.f64 x 2)))
(pow.f64 x 2)
(/.f64 (pow.f64 x 2) 1)
(pow.f64 x 2)
(/.f64 (pow.f64 x 2) (/.f64 (pow.f64 x 2) (pow.f64 x 2)))
(pow.f64 x 2)
(/.f64 (pow.f64 x 2) (/.f64 (/.f64 (pow.f64 x 2) (pow.f64 x 2)) (/.f64 (pow.f64 x 2) (pow.f64 x 2))))
(pow.f64 x 2)
(neg.f64 (neg.f64 (pow.f64 x 2)))
(pow.f64 x 2)

eval112.0ms (4.1%)

Compiler

Compiled 6077 to 5028 computations (17.3% saved)

prune27.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1963199
Fresh000
Picked101
Done112
Total1984202
Error
0.0b
Counts
202 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
0.8b
(*.f64 2 (atan.f64 (-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1)))
1.0b
(*.f64 2 (atan.f64 (-.f64 1 x)))
0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
2.0b
(*.f64 2 (atan.f64 1))
Compiler

Compiled 37 to 32 computations (13.5% saved)

localize4.0ms (0.1%)

Compiler

Compiled 9 to 9 computations (0% saved)

localize7.0ms (0.3%)

Compiler

Compiled 17 to 13 computations (23.5% saved)

localize20.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 x 2)
0.0b
(-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1)
0.0b
(*.f64 1/2 (pow.f64 x 2))
0.0b
(atan.f64 (-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1))
Compiler

Compiled 51 to 40 computations (21.6% saved)

series1.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@0
(atan.f64 (-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1))
0.0ms
x
@-inf
(atan.f64 (-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1))
0.0ms
x
@inf
(atan.f64 (-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1))
0.0ms
x
@0
(-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1)
0.0ms
x
@-inf
(-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1)

rewrite73.0ms (2.7%)

Algorithm
batch-egg-rewrite
Rules
1720×rational_best_oopsla_all_46_json_45_simplify-23
1074×rational_best_oopsla_all_46_json-2
1074×rational_best_oopsla_all_46_json-1
1074×rational_best_oopsla_all_46_json-4
1074×rational_best_oopsla_all_46_json-3
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01254
16754
214854
346454
4215554
Stop Event
node limit
Counts
2 → 93
Calls
Call 1
Inputs
(atan.f64 (-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1))
(-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1)
Outputs
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simplify107.0ms (4%)

Algorithm
egg-herbie
Rules
1058×rational_best_oopsla_all_46_json_45_simplify-49
928×rational_best_oopsla_all_46_json_45_simplify-82
904×rational_best_oopsla_all_46_json_45_simplify-72
682×rational_best_oopsla_all_46_json_45_simplify-35
650×rational_best_oopsla_all_46_json_45_simplify-89
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01846639
17056487
235295555
Stop Event
node limit
Counts
117 → 132
Calls
Call 1
Inputs
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
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(*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))))
(*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))))
(*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))))
(*.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) -1)
(*.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (neg.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))))
(*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 1 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))))
(*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))))
(*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (+.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) (/.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))))
(*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (+.f64 0 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 1 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))))))
(*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (+.f64 0 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))))))
(*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (*.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (/.f64 -1 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))))
(*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))))
(*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (*.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (/.f64 (neg.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))))
(*.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 1 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))
(*.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))
(*.f64 (neg.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))
(*.f64 (*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))))) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) 1)
(/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))
(/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))))
(/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))))))
(/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) -1)
(neg.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))
Outputs
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (neg.f64 x))
(-.f64 1 x)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x))
(-.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x))
(-.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))
(+.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) 0)
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(+.f64 0 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(-.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) 0)
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(-.f64 0 (neg.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 -1 (neg.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 -1 (*.f64 (/.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))) (neg.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))))))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) 1)
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) (/.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) (*.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) (/.f64 1 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))))))
(atan.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) (*.f64 (/.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))) (/.f64 (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))) (atan.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))))))
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(+.f64 (/.f64 (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))) (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2)))) (*.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) (/.f64 (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))) (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))))))
(*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))) (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2)))))
(*.f64 (*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (*.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))
(*.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)) (*.f64 (/.f64 (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))) (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)))) (*.f64 (/.f64 (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))) (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)))) (/.f64 (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))) (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)))))))
(*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (*.f64 (/.f64 (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))) (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2)))) (*.f64 (/.f64 (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))) (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2)))) (/.f64 (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))) (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2)))))))
(/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) 1)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))
(/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)))
(/.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)) (/.f64 (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))) (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)))))
(/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))) (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2)))))
(/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1)) (/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))))
(/.f64 (+.f64 1 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x)) (/.f64 (/.f64 (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))) (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)))) (/.f64 (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))) (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))))))
(/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (/.f64 (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))) (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2)))) (/.f64 (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))) (+.f64 x (+.f64 -1 (*.f64 (pow.f64 x 2) -1/2))))))
(/.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)))) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x)) (/.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))))))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (neg.f64 x)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (-.f64 1 x))
(/.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1) -1)
(neg.f64 (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))))
(+.f64 1 (neg.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))))
(-.f64 1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)))
(neg.f64 (+.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)) -1))
(neg.f64 (+.f64 -1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))))
(+.f64 1 (neg.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))))
(-.f64 1 (+.f64 x (*.f64 (pow.f64 x 2) -1/2)))

eval142.0ms (5.3%)

Compiler

Compiled 7817 to 6385 computations (18.3% saved)

prune31.0ms (1.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New2330233
Fresh000
Picked011
Done033
Total2334237
Error
0.0b
Counts
237 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
0.8b
(*.f64 2 (atan.f64 (-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1)))
1.0b
(*.f64 2 (atan.f64 (-.f64 1 x)))
0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
2.0b
(*.f64 2 (atan.f64 1))
Compiler

Compiled 37 to 32 computations (13.5% saved)

regimes15.0ms (0.6%)

Counts
6 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 1))
(*.f64 2 (atan.f64 (-.f64 1 x)))
(*.f64 2 (atan.f64 (+.f64 1 (neg.f64 x))))
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 2 (atan.f64 (-.f64 (-.f64 (*.f64 1/2 (pow.f64 x 2)) x) -1)))
(*.f64 2 (atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Calls

5 calls:

4.0ms
x
2.0ms
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
2.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
2.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
Results
ErrorSegmentsBranch
0.0b1x
0.0b1(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
0.0b1(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b1(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b1(/.f64 (-.f64 1 x) (+.f64 1 x))
Compiler

Compiled 96 to 79 computations (17.7% saved)

regimes5.0ms (0.2%)

Accuracy

Total -0.9b remaining (-89.9%)

Threshold costs -0.9b (-89.9%)

Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 1))
(*.f64 2 (atan.f64 (-.f64 1 x)))
(*.f64 2 (atan.f64 (+.f64 1 (neg.f64 x))))
Outputs
(*.f64 2 (atan.f64 (-.f64 1 x)))
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
1.0b1x
Compiler

Compiled 20 to 17 computations (15% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01661
Stop Event
done
saturated
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 2 (atan.f64 (-.f64 1 x)))
(*.f64 2 (atan.f64 1))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 2 (atan.f64 (-.f64 1 x)))
(*.f64 2 (atan.f64 1))
Compiler

Compiled 24 to 21 computations (12.5% saved)

soundness0.0ms (0%)

end83.0ms (3.1%)

Compiler

Compiled 22 to 19 computations (13.6% saved)

Profiling

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