Details

Time bar (total: 2.3s)

analyze65.0ms (2.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
37.5%62.4%0.1%6
37.5%40.6%22%7
43.7%32.8%23.5%8
54.6%21.9%23.5%9
58.5%17.2%24.3%10
64.4%11.3%24.3%11
66.5%8.8%24.7%12
Compiler

Compiled 8 to 5 computations (37.5% saved)

sample1.7s (73.3%)

Results
1.7s8256×body256valid
3.0ms37×body256invalid

preprocess39.0ms (1.7%)

Algorithm
egg-herbie
Rules
90×fma-neg_binary64
60×fma-def_binary64
24×cancel-sign-sub-inv_binary64
20×sub-neg_binary64
16×associate--r+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
11714
23114
35514
48214
515114
622914
731914
838314
939714
1039914
022
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(-.f64 x (*.f64 y y))
(-.f64 y (*.f64 x x))
Outputs
(-.f64 x (*.f64 y y))
(-.f64 y (*.f64 x x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify79.0ms (3.4%)

Algorithm
egg-herbie
Rules
65×fma-def_binary64
44×fma-neg_binary64
22×cancel-sign-sub-inv_binary64
15×sub-neg_binary64
11×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
1107
2187
3307
4457
5727
61167
71617
82097
92587
102967
113007
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(-.f64 x (*.f64 y y))
Outputs
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)

eval1.0ms (0%)

Compiler

Compiled 12 to 6 computations (50% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0b
Counts
3 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
0b
(fma.f64 y (neg.f64 y) x)
0.0b
(-.f64 x (*.f64 y y))
Compiler

Compiled 14 to 8 computations (42.9% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(-.f64 x (*.f64 y y))
Compiler

Compiled 12 to 4 computations (66.7% saved)

series3.0ms (0.1%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(-.f64 x (*.f64 y y))
1.0ms
y
@inf
(-.f64 x (*.f64 y y))
0.0ms
x
@inf
(-.f64 x (*.f64 y y))
0.0ms
y
@0
(-.f64 x (*.f64 y y))
0.0ms
y
@-inf
(-.f64 x (*.f64 y y))

rewrite47.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
613×pow1_binary64
573×add-log-exp_binary64
573×log1p-expm1-u_binary64
573×expm1-log1p-u_binary64
559×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11137
216087
Stop Event
node limit
Counts
1 → 35
Calls
Call 1
Inputs
(-.f64 x (*.f64 y y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 y (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (*.f64 y (neg.f64 y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (*.f64 y y)) (fma.f64 (*.f64 y (neg.f64 y)) 1 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (*.f64 y y)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 y y))) (cbrt.f64 (pow.f64 y 4)) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (neg.f64 y)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 x (*.f64 y y))) (pow.f64 (cbrt.f64 (-.f64 x (*.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 x (*.f64 y y))) 2) (cbrt.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 x (*.f64 y y))) (sqrt.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 x x (+.f64 (pow.f64 y 4) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 y 4)) (/.f64 1 (+.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 x) y) (-.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (+.f64 (pow.f64 y 4) (*.f64 x (*.f64 y y)))) (-.f64 (pow.f64 x 3) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x (*.f64 y y)) (-.f64 (*.f64 x x) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6)) (fma.f64 x x (+.f64 (pow.f64 y 4) (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 y 4)) (+.f64 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 6))) (neg.f64 (fma.f64 x x (+.f64 (pow.f64 y 4) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 y 4))) (neg.f64 (+.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 y (neg.f64 y)) 3)) (+.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 y (neg.f64 y)) (*.f64 y (neg.f64 y))) (*.f64 x (*.f64 y (neg.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y (neg.f64 y)) (*.f64 y (neg.f64 y)))) (-.f64 x (*.f64 y (neg.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 x (*.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 x (*.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 x (*.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 x (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 x (*.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 y (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 y (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 y (neg.f64 y)))))))

simplify101.0ms (4.4%)

Algorithm
egg-herbie
Rules
548×fma-neg_binary64
466×associate-*l*_binary64
434×unswap-sqr_binary64
413×cancel-sign-sub-inv_binary64
317×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
08165
117147
234147
369147
4156147
5446147
61611147
73270147
84794147
96092147
107177147
117909147
Stop Event
node limit
Counts
59 → 40
Calls
Call 1
Inputs
(*.f64 -1 (pow.f64 y 2))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
x
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
x
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
x
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(*.f64 -1 (pow.f64 y 2))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(*.f64 -1 (pow.f64 y 2))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
Outputs
(*.f64 -1 (pow.f64 y 2))
(neg.f64 (*.f64 y y))
(*.f64 y (neg.f64 y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
x
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
x
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
x
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(*.f64 -1 (pow.f64 y 2))
(neg.f64 (*.f64 y y))
(*.f64 y (neg.f64 y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(*.f64 -1 (pow.f64 y 2))
(neg.f64 (*.f64 y y))
(*.f64 y (neg.f64 y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) x)
(fma.f64 -1 (*.f64 y y) x)
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)

localize5.0ms (0.2%)

Compiler

Compiled 11 to 4 computations (63.6% saved)

eval28.0ms (1.2%)

Compiler

Compiled 455 to 165 computations (63.7% saved)

prune7.0ms (0.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New38240
Fresh000
Picked011
Done011
Total38442
Error
0b
Counts
42 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
19.8b
x
0b
(fma.f64 y (neg.f64 y) x)
42.9b
(*.f64 y (neg.f64 y))
0.0b
(-.f64 x (*.f64 y y))
Compiler

Compiled 23 to 14 computations (39.1% saved)

localize4.0ms (0.2%)

Compiler

Compiled 9 to 4 computations (55.6% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked011
Done022
Total044
Error
0b
Counts
4 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
19.8b
x
0b
(fma.f64 y (neg.f64 y) x)
42.9b
(*.f64 y (neg.f64 y))
0.0b
(-.f64 x (*.f64 y y))
Compiler

Compiled 23 to 14 computations (39.1% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done033
Total044
Error
0b
Counts
4 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
19.8b
x
0b
(fma.f64 y (neg.f64 y) x)
42.9b
(*.f64 y (neg.f64 y))
0.0b
(-.f64 x (*.f64 y y))
Compiler

Compiled 23 to 14 computations (39.1% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done033
Total044
Error
0b
Counts
4 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
19.8b
x
0b
(fma.f64 y (neg.f64 y) x)
42.9b
(*.f64 y (neg.f64 y))
0.0b
(-.f64 x (*.f64 y y))
Compiler

Compiled 23 to 14 computations (39.1% saved)

regimes24.0ms (1.1%)

Counts
4 → 1
Calls
Call 1
Inputs
x
(*.f64 y (neg.f64 y))
(-.f64 x (*.f64 y y))
(fma.f64 y (neg.f64 y) x)
Outputs
(fma.f64 y (neg.f64 y) x)
Calls

5 calls:

7.0ms
(*.f64 y y)
5.0ms
x
4.0ms
(-.f64 x (*.f64 y y))
4.0ms
y
3.0ms
(*.f64 y y)
Results
ErrorSegmentsBranch
0b1x
0b1y
0b1(-.f64 x (*.f64 y y))
0b1(*.f64 y y)
0b1(*.f64 y y)
Compiler

Compiled 40 to 21 computations (47.5% saved)

regimes15.0ms (0.7%)

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

4 calls:

4.0ms
x
4.0ms
(-.f64 x (*.f64 y y))
4.0ms
y
3.0ms
(*.f64 y y)
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1(-.f64 x (*.f64 y y))
0.0b1(*.f64 y y)
Compiler

Compiled 30 to 17 computations (43.3% saved)

regimes73.0ms (3.2%)

Accuracy

Total -54.5b remaining (-754.5%)

Threshold costs -54.5b (-754.5%)

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

2 calls:

61.0ms
x
11.0ms
y
Results
ErrorSegmentsBranch
16.1b5x
7.2b3y
Compiler

Compiled 13 to 8 computations (38.5% saved)

bsearch28.0ms (1.2%)

Algorithm
binary-search
Steps
TimeLeftRight
14.0ms
2.4433472610422326e+30
8.480132287102279e+30
14.0ms
-5228154425.392553
-26645.395865376613
Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify5.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01540
12440
22940
33240
43340
Stop Event
fuel
saturated
Calls
Call 1
Inputs
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(if (<=.f64 y -2741058627380211/524288) (*.f64 y (neg.f64 y)) (if (<=.f64 y 2443347261042232586804362477568) x (*.f64 y (neg.f64 y))))
x
Outputs
(fma.f64 y (neg.f64 y) x)
(-.f64 x (*.f64 y y))
(if (<=.f64 y -2741058627380211/524288) (*.f64 y (neg.f64 y)) (if (<=.f64 y 2443347261042232586804362477568) x (*.f64 y (neg.f64 y))))
x
Compiler

Compiled 36 to 20 computations (44.4% saved)

soundness50.0ms (2.2%)

Algorithm
egg-herbie
Rules
65×fma-def_binary64
44×fma-neg_binary64
22×cancel-sign-sub-inv_binary64
15×sub-neg_binary64
11×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
1107
2187
3307
4457
5727
61167
71617
82097
92587
102967
113007
Stop Event
saturated
Compiler

Compiled 38 to 23 computations (39.5% saved)

end32.0ms (1.4%)

Compiler

Compiled 30 to 13 computations (56.7% saved)

Profiling

Loading profile data...