Details

Time bar (total: 1.3s)

analyze3.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%25%25%4
62.5%12.5%25%5
68.7%6.2%25%6
71.8%3.1%25%7
73.4%1.6%25%8
74.2%0.8%25%9
74.6%0.4%25%10
74.8%0.2%25%11
74.9%0.1%25%12
Compiler

Compiled 7 to 5 computations (28.6% saved)

sample943.0ms (70.8%)

Results
930.0ms8256×body256valid
0.0msbody256invalid

preprocess22.0ms (1.7%)

Algorithm
egg-herbie
Rules
92×fma-def_binary64
68×fma-neg_binary64
24×cancel-sign-sub-inv_binary64
16×distribute-rgt-in_binary64
12×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
1117
2177
3227
4267
5317
6427
7647
81357
92547
103647
113867
123887
011
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(*.f64 x (-.f64 x 1))
Outputs
(*.f64 x (-.f64 x 1))
(*.f64 x (+.f64 x -1))
(fma.f64 x x (neg.f64 x))
(-.f64 (*.f64 x x) x)
Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify13.0ms (1%)

Algorithm
egg-herbie
Rules
92×fma-def_binary64
68×fma-neg_binary64
24×cancel-sign-sub-inv_binary64
16×distribute-rgt-in_binary64
12×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
1117
2177
3227
4267
5317
6427
7647
81357
92547
103647
113867
123887
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(*.f64 x (-.f64 x 1))
Outputs
(*.f64 x (-.f64 x 1))
(*.f64 x (+.f64 x -1))
(fma.f64 x x (neg.f64 x))
(-.f64 (*.f64 x x) x)

eval1.0ms (0%)

Compiler

Compiled 11 to 6 computations (45.5% 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
0.0b
(-.f64 (*.f64 x x) x)
0.0b
(*.f64 x (-.f64 x 1))
Compiler

Compiled 12 to 7 computations (41.7% saved)

localize3.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(*.f64 x (-.f64 x 1))
0.0b
(*.f64 x (-.f64 x 1))

series2.0ms (0.2%)

Counts
1 → 12
Calls

3 calls:

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

rewrite45.0ms (3.3%)

Algorithm
batch-egg-rewrite
Rules
507×pow1_binary64
492×add-sqr-sqrt_binary64
473×add-log-exp_binary64
472×log1p-expm1-u_binary64
472×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11057
213217
Stop Event
node limit
Counts
1 → 17
Calls
Call 1
Inputs
(*.f64 x (-.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) -1) x) (fma.f64 x x (+.f64 x 1)))))) (#(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 (pow.f64 x 3) -1)) (fma.f64 x x (+.f64 x 1)))))) (#(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 -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 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 -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (+.f64 x -1))))))))

simplify67.0ms (5.1%)

Algorithm
egg-herbie
Rules
679×fma-neg_binary64
545×associate-*l*_binary64
434×unswap-sqr_binary64
429×associate-*r*_binary64
355×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0783
11674
23274
37074
419374
571074
6346274
7755074
Stop Event
node limit
Counts
29 → 23
Calls
Call 1
Inputs
(*.f64 -1 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
Outputs
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))

localize3.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite43.0ms (3.3%)

Algorithm
batch-egg-rewrite
Rules
497×pow1_binary64
483×add-sqr-sqrt_binary64
468×add-log-exp_binary64
468×log1p-expm1-u_binary64
468×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047
1917
213167
Stop Event
node limit
Counts
1 → 36
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 x x) x) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 x x) x) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 x x) x) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.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 (-.f64 (*.f64 x x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (*.f64 x x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 2) (cbrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) (sqrt.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 6) (pow.f64 x 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (*.f64 x (fma.f64 x x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (*.f64 x x)) (/.f64 1 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (sqrt.f64 x)) (-.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 x (fma.f64 x x x))) (-.f64 (pow.f64 x 6) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x 4) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) (pow.f64 x 3)) (+.f64 (pow.f64 x 4) (*.f64 x (fma.f64 x x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 x x)) (fma.f64 x x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 x 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 x (fma.f64 x x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 x x))) (neg.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (neg.f64 x) 3)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (*.f64 x x) (neg.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (neg.f64 x) (neg.f64 x))) (-.f64 (*.f64 x x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 x x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 x x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (*.f64 x x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (*.f64 x x) x)))))))

simplify64.0ms (4.8%)

Algorithm
egg-herbie
Rules
679×fma-neg_binary64
545×associate-*l*_binary64
434×unswap-sqr_binary64
429×associate-*r*_binary64
355×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0783
11674
23274
37074
419374
571074
6346274
7755074
Stop Event
node limit
Counts
48 → 42
Calls
Call 1
Inputs
(*.f64 -1 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
Outputs
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(*.f64 x (+.f64 -1 x))

eval14.0ms (1%)

Compiler

Compiled 596 to 280 computations (53% saved)

prune10.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New63265
Fresh000
Picked011
Done011
Total63467
Error
0b
Counts
67 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
0.0b
(-.f64 (*.f64 x x) x)
0.0b
(*.f64 x (-.f64 x 1))
40.6b
(*.f64 x x)
21.6b
(neg.f64 x)
Compiler

Compiled 19 to 11 computations (42.1% saved)

localize2.0ms (0.2%)

localize2.0ms (0.1%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 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 (*.f64 x x) x)
0.0b
(*.f64 x (-.f64 x 1))
40.6b
(*.f64 x x)
21.6b
(neg.f64 x)
Compiler

Compiled 19 to 11 computations (42.1% saved)

regimes11.0ms (0.8%)

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

2 calls:

6.0ms
(*.f64 x (-.f64 x 1))
4.0ms
x
Results
ErrorSegmentsBranch
0.0b1x
0.0b1(*.f64 x (-.f64 x 1))
Compiler

Compiled 24 to 12 computations (50% saved)

regimes5.0ms (0.4%)

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

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
0.0b1x
Compiler

Compiled 13 to 5 computations (61.5% saved)

regimes10.0ms (0.8%)

Accuracy

Total -59.1b remaining (-3914.7%)

Threshold costs -59.1b (-3914.7%)

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

1 calls:

10.0ms
x
Results
ErrorSegmentsBranch
1.5b3x
Compiler

Compiled 8 to 4 computations (50% saved)

bsearch29.0ms (2.2%)

Algorithm
binary-search
Steps
TimeLeftRight
14.0ms
2.4692119590990748e-6
725097.1965075866
15.0ms
-2.4099437760197047
-0.4940573068275024
Compiler

Compiled 10 to 7 computations (30% saved)

simplify4.0ms (0.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01540
12440
22840
32940
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 x (-.f64 x 1))
(-.f64 (*.f64 x x) x)
(if (<=.f64 x -2713355472916547/1125899906842624) (*.f64 x x) (if (<=.f64 x 2915130948687591/1180591620717411303424) (neg.f64 x) (*.f64 x x)))
(neg.f64 x)
Outputs
(*.f64 x (-.f64 x 1))
(*.f64 x (+.f64 x -1))
(-.f64 (*.f64 x x) x)
(if (<=.f64 x -2713355472916547/1125899906842624) (*.f64 x x) (if (<=.f64 x 2915130948687591/1180591620717411303424) (neg.f64 x) (*.f64 x x)))
(neg.f64 x)

end31.0ms (2.4%)

Stop Event
done
Compiler

Compiled 61 to 31 computations (49.2% saved)

Profiling

Loading profile data...