Details

Time bar (total: 1.8s)

analyze58.0ms (3.2%)

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
56.2%43.7%0.1%7
56.2%32.8%11%8
65.6%22.6%11.8%9
65.6%16.8%17.7%10
70.2%11.5%18.2%11
70.2%8.5%21.3%12
Compiler

Compiled 10 to 7 computations (30% saved)

sample983.0ms (54.1%)

Results
932.0ms8255×body256valid
39.0ms412×body256invalid
0.0msbody1024valid

preprocess67.0ms (3.7%)

Algorithm
egg-herbie
Rules
330×fma-def_binary64
192×fma-neg_binary64
60×cancel-sign-sub-inv_binary64
56×distribute-rgt-in_binary64
37×associate-*r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01020
11820
23820
38220
414720
521020
639120
769220
8108520
9119120
10120920
022
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(*.f64 1/2 (-.f64 (*.f64 x x) y))
(*.f64 1/2 (-.f64 (*.f64 y y) x))
Outputs
(*.f64 1/2 (-.f64 (*.f64 x x) y))
(*.f64 1/2 (-.f64 (*.f64 y y) x))
(*.f64 1/2 (fma.f64 y y (neg.f64 x)))
Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify21.0ms (1.2%)

Algorithm
egg-herbie
Rules
230×fma-def_binary64
111×fma-neg_binary64
43×distribute-rgt-in_binary64
39×cancel-sign-sub-inv_binary64
28×distribute-lft-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11110
22210
34810
48410
511810
620910
735710
855210
972210
1082210
1183810
Stop Event
saturated
Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 1/2 (-.f64 (*.f64 x x) y))
Outputs
(*.f64 1/2 (-.f64 (*.f64 x x) y))

eval0.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% 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 1/2 (-.f64 (*.f64 x x) y))
Compiler

Compiled 9 to 6 computations (33.3% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiled 20 to 7 computations (65% saved)

series3.0ms (0.1%)

Counts
1 → 24
Calls

6 calls:

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

rewrite47.0ms (2.6%)

Algorithm
batch-egg-rewrite
Rules
597×pow1_binary64
558×add-log-exp_binary64
558×log1p-expm1-u_binary64
558×expm1-log1p-u_binary64
544×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11117
215367
Stop Event
node limit
Counts
1 → 35
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) y)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 (neg.f64 y) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 y) 1 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 x x) y) (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 y) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (*.f64 x x) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (*.f64 x x) y)) (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) y)) 2) (cbrt.f64 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 x x) y)) (sqrt.f64 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (/.f64 1 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (sqrt.f64 y)) (-.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y))) (-.f64 (pow.f64 x 6) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x y) (-.f64 (pow.f64 x 4) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (neg.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (neg.f64 y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (neg.f64 y) (neg.f64 y)) (*.f64 (*.f64 x x) (neg.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (neg.f64 y) (neg.f64 y))) (-.f64 (*.f64 x x) (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 x x) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 x x) y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (*.f64 x x) y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (neg.f64 y))))))

simplify87.0ms (4.8%)

Algorithm
egg-herbie
Rules
706×distribute-rgt-neg-in_binary64
541×distribute-lft-neg-in_binary64
511×fma-neg_binary64
434×unswap-sqr_binary64
424×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
08183
116147
229147
345147
496147
5281147
61170147
73169147
85504147
97088147
107955147
Stop Event
node limit
Counts
59 → 40
Calls
Call 1
Inputs
(*.f64 -1 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(*.f64 -1 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(*.f64 -1 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
Outputs
(*.f64 -1 y)
(neg.f64 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(*.f64 -1 y)
(neg.f64 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(*.f64 -1 y)
(neg.f64 y)
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))
(+.f64 (pow.f64 x 2) (*.f64 -1 y))
(+.f64 (neg.f64 y) (*.f64 x x))
(-.f64 (*.f64 x x) y)
(fma.f64 x x (neg.f64 y))

eval9.0ms (0.5%)

Compiler

Compiled 497 to 246 computations (50.5% saved)

prune7.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New37340
Fresh000
Picked011
Done000
Total37441
Error
0b
Counts
41 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
0.0b
(*.f64 1/2 (-.f64 (*.f64 x x) y))
39.0b
(*.f64 1/2 (*.f64 x x))
0b
(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
23.7b
(*.f64 1/2 (neg.f64 y))
Compiler

Compiled 31 to 22 computations (29% saved)

localize4.0ms (0.2%)

Compiler

Compiled 10 to 6 computations (40% saved)

localize5.0ms (0.3%)

Compiler

Compiled 12 to 6 computations (50% saved)

localize7.0ms (0.4%)

Compiler

Compiled 19 to 7 computations (63.2% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done033
Total044
Error
0b
Counts
4 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
0.0b
(*.f64 1/2 (-.f64 (*.f64 x x) y))
39.0b
(*.f64 1/2 (*.f64 x x))
0b
(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
23.7b
(*.f64 1/2 (neg.f64 y))
Compiler

Compiled 31 to 22 computations (29% saved)

regimes126.0ms (6.9%)

Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 1/2 (neg.f64 y))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (-.f64 (*.f64 x x) y))
(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
Outputs
(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
Calls

6 calls:

107.0ms
y
4.0ms
(*.f64 1/2 (-.f64 (*.f64 x x) y))
4.0ms
(-.f64 (*.f64 x x) y)
4.0ms
x
3.0ms
(*.f64 x x)
Results
ErrorSegmentsBranch
0b1x
0b1y
0b1(*.f64 1/2 (-.f64 (*.f64 x x) y))
0b1(-.f64 (*.f64 x x) y)
0b1(*.f64 x x)
0b1(*.f64 x x)
Compiler

Compiled 57 to 34 computations (40.4% saved)

regimes20.0ms (1.1%)

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

5 calls:

5.0ms
x
4.0ms
(*.f64 1/2 (-.f64 (*.f64 x x) y))
4.0ms
(-.f64 (*.f64 x x) y)
4.0ms
y
3.0ms
(*.f64 x x)
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1(*.f64 1/2 (-.f64 (*.f64 x x) y))
0.0b1(-.f64 (*.f64 x x) y)
0.0b1(*.f64 x x)
Compiler

Compiled 45 to 28 computations (37.8% saved)

regimes39.0ms (2.2%)

Accuracy

Total -51.5b remaining (-507.5%)

Threshold costs -51.5b (-507.5%)

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

3 calls:

20.0ms
y
11.0ms
x
6.0ms
(*.f64 x x)
Results
ErrorSegmentsBranch
10.2b3x
15.8b7y
11.1b2(*.f64 x x)
Compiler

Compiled 22 to 15 computations (31.8% saved)

bsearch30.0ms (1.7%)

Algorithm
binary-search
Steps
TimeLeftRight
15.0ms
3.428143198451247e-31
1.026949912677751e-25
15.0ms
-7.323139487666682e+35
-2.830798111213867e+34
Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify7.0ms (0.4%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01958
13054
24054
34454
44554
Stop Event
done
saturated
Calls
Call 1
Inputs
(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
(*.f64 1/2 (-.f64 (*.f64 x x) y))
(if (<=.f64 x -732313948766668151249816894046208000) (*.f64 1/2 (*.f64 x x)) (if (<=.f64 x 7828495152408275/22835963083295358096932575511191922182123945984) (*.f64 1/2 (neg.f64 y)) (*.f64 1/2 (*.f64 x x))))
(*.f64 1/2 (neg.f64 y))
Outputs
(*.f64 1/2 (fma.f64 x x (neg.f64 y)))
(*.f64 1/2 (-.f64 (*.f64 x x) y))
(if (<=.f64 x -732313948766668151249816894046208000) (*.f64 1/2 (*.f64 x x)) (if (<=.f64 x 7828495152408275/22835963083295358096932575511191922182123945984) (*.f64 1/2 (neg.f64 y)) (*.f64 1/2 (*.f64 x x))))
(if (<=.f64 x -732313948766668151249816894046208000) (*.f64 1/2 (*.f64 x x)) (if (<=.f64 x 7828495152408275/22835963083295358096932575511191922182123945984) (*.f64 -1/2 y) (*.f64 1/2 (*.f64 x x))))
(if (<=.f64 x -732313948766668151249816894046208000) (*.f64 1/2 (*.f64 x x)) (if (<=.f64 x 7828495152408275/22835963083295358096932575511191922182123945984) (*.f64 y -1/2) (*.f64 1/2 (*.f64 x x))))
(*.f64 1/2 (neg.f64 y))
(*.f64 -1/2 y)
(*.f64 y -1/2)
Compiler

Compiled 46 to 31 computations (32.6% saved)

soundness255.0ms (14%)

Algorithm
egg-herbie
Rules
706×distribute-rgt-neg-in_binary64
541×distribute-lft-neg-in_binary64
511×fma-neg_binary64
434×unswap-sqr_binary64
424×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
08183
116147
229147
345147
496147
5281147
61170147
73169147
85504147
97088147
107955147
Stop Event
node limit
Compiler

Compiled 33 to 22 computations (33.3% saved)

end33.0ms (1.8%)

Compiler

Compiled 40 to 24 computations (40% saved)

Profiling

Loading profile data...