Details

Time bar (total: 1.1s)

analyze4.0ms (0.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%37.5%12.5%4
62.5%18.7%18.8%5
68.7%9.4%21.9%6
71.8%4.7%23.5%7
73.4%2.3%24.3%8
74.2%1.2%24.6%9
74.6%0.6%24.8%10
74.8%0.3%24.9%11
74.9%0.1%25%12
Compiler

Compiled 7 to 4 computations (42.9% saved)

sample596.0ms (53%)

Results
583.0ms8256×body256valid
0.0ms7×body256invalid

preprocess17.0ms (1.5%)

Algorithm
2×egg-herbie
Rules
9×fma-def_binary64
2×+-commutative_binary64
2×associate-*l*_binary64
2×distribute-lft-in_binary64
2×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047
185
2135
3195
4235
5335
6355
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(+.f64 x (*.f64 x x))
Outputs
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify7.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
9×fma-def_binary64
2×+-commutative_binary64
2×associate-*l*_binary64
2×distribute-lft-in_binary64
2×distribute-rgt-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
047
185
2135
3195
4235
5335
6355
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(+.f64 x (*.f64 x x))
Outputs
(+.f64 x (*.f64 x x))
(fma.f64 x x x)

eval0.0ms (0%)

Compiler

Compiled 10 to 4 computations (60% 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 x x x)
▶0.0b
(+.f64 x (*.f64 x x))
Compiler

Compiled 11 to 5 computations (54.5% saved)

localize7.0ms (0.6%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 x (*.f64 x x))
✓0.0b
(+.f64 x (*.f64 x x))

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite38.0ms (3.4%)

Algorithm
1×batch-egg-rewrite
Rules
502×pow1_binary64
488×add-sqr-sqrt_binary64
474×add-log-exp_binary64
473×log1p-expm1-u_binary64
473×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
047
1925
213815
Stop Event
1×node limit
Counts
1 → 38
Calls
Call 1
Inputs
(+.f64 x (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 x x))) (/.f64 (pow.f64 x 4) (-.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x x)) (pow.f64 (cbrt.f64 (fma.f64 x x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) 2) (cbrt.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (/.f64 1 (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 x 4)) (/.f64 1 (-.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x 1) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x 1) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3))) (+.f64 (pow.f64 x 3) (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (*.f64 x x)) (-.f64 (*.f64 x x) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 x x) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 x 4)) (-.f64 x (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6))) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 x 4))) (neg.f64 (-.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 x x)) (-.f64 (*.f64 x x) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x x)))))))

simplify125.0ms (11.2%)

Algorithm
1×egg-herbie
Rules
1107×sqr-pow_binary64
739×fma-def_binary64
573×cube-prod_binary64
564×fabs-mul_binary64
536×pow-sqr_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0572
11154
22254
33954
48954
526654
692054
7209654
8250354
9271854
10295454
11330354
12373954
13424054
14481954
15554054
16638954
17678354
18707154
19735454
20742854
21746454
Stop Event
1×node limit
Counts
50 → 42
Calls
Call 1
Inputs
x
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
Outputs
x
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)

localize2.0ms (0.2%)

eval8.0ms (0.7%)

Compiler

Compiled 401 to 185 computations (53.9% saved)

prune7.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New39342
Fresh000
Picked101
Done011
Total40444
Error
0b
Counts
44 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶41.9b
(*.f64 x x)
21.0b
x
▶0.0b
(*.f64 (+.f64 x 1) x)
✓0.0b
(+.f64 x (*.f64 x x))
Compiler

Compiled 18 to 10 computations (44.4% saved)

localize3.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (+.f64 x 1) x)
✓0.0b
(*.f64 (+.f64 x 1) x)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(*.f64 (+.f64 x 1) x)
1.0ms
x
@-inf
(*.f64 (+.f64 x 1) x)
0.0ms
x
@inf
(*.f64 (+.f64 x 1) x)

rewrite36.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
502×pow1_binary64
487×add-sqr-sqrt_binary64
468×log1p-expm1-u_binary64
468×expm1-log1p-u_binary64
467×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11037
212947
Stop Event
1×node limit
Counts
1 → 17
Calls
Call 1
Inputs
(*.f64 (+.f64 x 1) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 x 3)) x) (fma.f64 x x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 x x -1) x) (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (fma.f64 x x -1)) (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (*.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 x) (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (*.f64 x x))))))))

simplify126.0ms (11.2%)

Algorithm
1×egg-herbie
Rules
1107×sqr-pow_binary64
739×fma-def_binary64
573×cube-prod_binary64
564×fabs-mul_binary64
536×pow-sqr_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0572
11154
22254
33954
48954
526654
692054
7209654
8250354
9271854
10295454
11330354
12373954
13424054
14481954
15554054
16638954
17678354
18707154
19735454
20742854
21746454
Stop Event
1×node limit
Counts
29 → 22
Calls
Call 1
Inputs
x
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
Outputs
x
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)

localize2.0ms (0.2%)

eval6.0ms (0.6%)

Compiler

Compiled 159 to 75 computations (52.8% saved)

prune4.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New22022
Fresh011
Picked011
Done022
Total22426
Error
0b
Counts
26 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓41.9b
(*.f64 x x)
21.0b
x
✓0.0b
(*.f64 (+.f64 x 1) x)
✓0.0b
(+.f64 x (*.f64 x x))
Compiler

Compiled 18 to 10 computations (44.4% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 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
✓41.9b
(*.f64 x x)
21.0b
x
✓0.0b
(*.f64 (+.f64 x 1) x)
✓0.0b
(+.f64 x (*.f64 x x))
Compiler

Compiled 18 to 10 computations (44.4% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 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
✓41.9b
(*.f64 x x)
21.0b
x
✓0.0b
(*.f64 (+.f64 x 1) x)
✓0.0b
(+.f64 x (*.f64 x x))
Compiler

Compiled 18 to 10 computations (44.4% saved)

regimes12.0ms (1%)

Counts
5 → 1
Calls
Call 1
Inputs
x
(*.f64 x x)
(*.f64 (+.f64 x 1) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
Outputs
(fma.f64 x x x)
Calls

2 calls:

6.0ms
(+.f64 x (*.f64 x x))
5.0ms
x
Results
ErrorSegmentsBranch
0b1x
0b1(+.f64 x (*.f64 x x))
Compiler

Compiled 27 to 11 computations (59.3% saved)

regimes10.0ms (0.9%)

Counts
4 → 1
Calls
Call 1
Inputs
x
(*.f64 x x)
(*.f64 (+.f64 x 1) x)
(+.f64 x (*.f64 x x))
Outputs
(+.f64 x (*.f64 x x))
Calls

2 calls:

5.0ms
(+.f64 x (*.f64 x x))
4.0ms
x
Results
ErrorSegmentsBranch
0.0b1x
0.0b1(+.f64 x (*.f64 x x))
Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes5.0ms (0.5%)

Counts
3 → 1
Calls
Call 1
Inputs
x
(*.f64 x x)
(*.f64 (+.f64 x 1) x)
Outputs
(*.f64 (+.f64 x 1) x)
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
0.0b1x
Compiler

Compiled 12 to 6 computations (50% saved)

regimes10.0ms (0.9%)

Accuracy

Total -58.2b remaining (-2464.2%)

Threshold costs -58.2b (-2464.2%)

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

1 calls:

10.0ms
x
Results
ErrorSegmentsBranch
2.4b3x
Compiler

Compiled 7 to 3 computations (57.1% saved)

bsearch47.0ms (4.2%)

Algorithm
2×binary-search
Steps
TimeLeftRight
33.0ms
2.6903770676420974e-8
3.9014726948501264
14.0ms
-10.370301521808003
-5.185064830304864e-6
Compiler

Compiled 10 to 6 computations (40% saved)

simplify3.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
2×+-commutative_binary64
1×*-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01541
12041
Stop Event
1×saturated
Calls
Call 1
Inputs
(fma.f64 x x x)
(+.f64 x (*.f64 x x))
(*.f64 (+.f64 x 1) x)
(if (<=.f64 x -729745094833347/70368744177664) (*.f64 x x) (if (<=.f64 x 8131165753929063/302231454903657293676544) x (*.f64 x x)))
x
Outputs
(fma.f64 x x x)
(+.f64 x (*.f64 x x))
(*.f64 (+.f64 x 1) x)
(*.f64 x (+.f64 x 1))
(if (<=.f64 x -729745094833347/70368744177664) (*.f64 x x) (if (<=.f64 x 8131165753929063/302231454903657293676544) x (*.f64 x x)))
x

end39.0ms (3.4%)

Stop Event
1×fuel
Compiler

Compiled 66 to 31 computations (53% saved)

Profiling

Loading profile data...