Details

Time bar (total: 1.6s)

analyze4.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
75%12.5%12.5%5
75%6.2%18.8%6
75%3.1%21.9%7
75%1.6%23.5%8
75%0.8%24.3%9
75%0.4%24.6%10
75%0.2%24.8%11
75%0.1%24.9%12
75%0%25%13
75%0%25%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample849.0ms (53.4%)

Results
836.0ms8256×body128valid
Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess16.0ms (1%)

Algorithm
2×egg-herbie
Rules
3×fma-neg_binary64
2×+-commutative_binary64
2×sub-neg_binary64
1×*-commutative_binary64
1×associate-/l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1158
2218
3248
4268
5278
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (-.f64 (*.f64 x x) 3) 6)
Outputs
(/.f64 (-.f64 (*.f64 x x) 3) 6)
(/.f64 (fma.f64 x x -3) 6)
(fma.f64 (/.f64 x 6) x -1/2)
Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
3×fma-neg_binary64
2×+-commutative_binary64
2×sub-neg_binary64
1×*-commutative_binary64
1×associate-/l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1158
2218
3248
4268
5278
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 x x) 3) 6)
Outputs
(/.f64 (-.f64 (*.f64 x x) 3) 6)
(/.f64 (fma.f64 x x -3) 6)
(fma.f64 (/.f64 x 6) x -1/2)

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.1b
(fma.f64 (/.f64 x 6) x -1/2)
▶0.1b
(/.f64 (-.f64 (*.f64 x x) 3) 6)
Compiler

Compiled 44 to 32 computations (27.3% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (*.f64 x x) 3)
✓0.1b
(/.f64 (-.f64 (*.f64 x x) 3) 6)

series3.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 (-.f64 (*.f64 x x) 3) 6)
1.0ms
x
@0
(/.f64 (-.f64 (*.f64 x x) 3) 6)
0.0ms
x
@-inf
(/.f64 (-.f64 (*.f64 x x) 3) 6)
0.0ms
x
@inf
(-.f64 (*.f64 x x) 3)
0.0ms
x
@0
(-.f64 (*.f64 x x) 3)

rewrite68.0ms (4.3%)

Algorithm
1×batch-egg-rewrite
Rules
796×pow1_binary64
756×log1p-expm1-u_binary64
756×expm1-log1p-u_binary64
82×add-sqr-sqrt_binary64
78×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
116613
2203313
Stop Event
1×node limit
Counts
2 → 59
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 x x) 3) 6)
(-.f64 (*.f64 x x) 3)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) 1/6) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (*.f64 x x) 1/6) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (fma.f64 x x -3) 1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x -3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (fma.f64 x x -3) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (fma.f64 x x -3) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -3)) 2) (*.f64 (cbrt.f64 (fma.f64 x x -3)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) (pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) 2) (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x x -3)) (*.f64 (sqrt.f64 (fma.f64 x x -3)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) (sqrt.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (fma.f64 x x -3)) -1/6)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/6 (fma.f64 x x -3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 x x -3) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (fma.f64 x x -3) 1/6) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (fma.f64 x x -3) -6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (fma.f64 x x -3) 2) 1/36))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (fma.f64 x x -3) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (fma.f64 x x -3) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 x x -3) 1/6)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) -3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -3 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x -3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x -3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x -3)) (pow.f64 (cbrt.f64 (fma.f64 x x -3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -3)) 2) (cbrt.f64 (fma.f64 x x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x x -3)) (sqrt.f64 (fma.f64 x x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 6) -27) (/.f64 1 (+.f64 (+.f64 (pow.f64 x 4) 9) (*.f64 x (*.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 4) -9) (/.f64 1 (fma.f64 x x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 (pow.f64 x 4) 9) (*.f64 x (*.f64 x 3))) (+.f64 (pow.f64 x 6) -27)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x 3) (+.f64 (pow.f64 x 4) -9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) -27) (+.f64 (+.f64 (pow.f64 x 4) 9) (*.f64 x (*.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) -27) (+.f64 (pow.f64 x 4) (-.f64 9 (*.f64 (*.f64 x x) -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 4) -9) (fma.f64 x x 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 4) -9) (-.f64 (*.f64 x x) -3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 6) -27)) (neg.f64 (+.f64 (+.f64 (pow.f64 x 4) 9) (*.f64 x (*.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 4) -9)) (neg.f64 (fma.f64 x x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x -3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x -3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x x -3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x -3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x -3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x -3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) -3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) -3)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x x -3)) 1))))))

simplify62.0ms (3.9%)

Algorithm
1×egg-herbie
Rules
608×sqr-pow_binary64
442×associate-*l*_binary64
434×unswap-sqr_binary64
281×cube-prod_binary64
275×fabs-mul_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
012159
123141
238141
362141
4127141
5358141
61247141
72167141
82351141
92535141
102743141
113036141
123429141
133907141
144468141
Stop Event
1×node limit
Counts
83 → 68
Calls
Call 1
Inputs
-1/2
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(*.f64 1/6 (pow.f64 x 2))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(*.f64 1/6 (pow.f64 x 2))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
-3
(-.f64 (pow.f64 x 2) 3)
(-.f64 (pow.f64 x 2) 3)
(-.f64 (pow.f64 x 2) 3)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 3)
(-.f64 (pow.f64 x 2) 3)
(-.f64 (pow.f64 x 2) 3)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 3)
(-.f64 (pow.f64 x 2) 3)
(-.f64 (pow.f64 x 2) 3)
Outputs
-1/2
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 1/6 x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 1/6 x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 1/6 x) -1/2)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 1/6 x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 1/6 x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 1/6 x) -1/2)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 1/6 x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 1/6 x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 1/6 x) -1/2)
-3
(-.f64 (pow.f64 x 2) 3)
(+.f64 (*.f64 x x) -3)
(fma.f64 x x -3)
(-.f64 (pow.f64 x 2) 3)
(+.f64 (*.f64 x x) -3)
(fma.f64 x x -3)
(-.f64 (pow.f64 x 2) 3)
(+.f64 (*.f64 x x) -3)
(fma.f64 x x -3)
(pow.f64 x 2)
(*.f64 x x)
(-.f64 (pow.f64 x 2) 3)
(+.f64 (*.f64 x x) -3)
(fma.f64 x x -3)
(-.f64 (pow.f64 x 2) 3)
(+.f64 (*.f64 x x) -3)
(fma.f64 x x -3)
(-.f64 (pow.f64 x 2) 3)
(+.f64 (*.f64 x x) -3)
(fma.f64 x x -3)
(pow.f64 x 2)
(*.f64 x x)
(-.f64 (pow.f64 x 2) 3)
(+.f64 (*.f64 x x) -3)
(fma.f64 x x -3)
(-.f64 (pow.f64 x 2) 3)
(+.f64 (*.f64 x x) -3)
(fma.f64 x x -3)
(-.f64 (pow.f64 x 2) 3)
(+.f64 (*.f64 x x) -3)
(fma.f64 x x -3)

prune54.0ms (3.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New64468
Fresh011
Picked011
Done000
Total64670
Error
0.0b
Counts
70 → 6
Alt Table
StatusErrorProgram
10.6b
(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -9) (fma.f64 x x 3)) 6)
0.1b
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
▶0.1b
(fma.f64 (/.f64 x 6) x -1/2)
0.4b
(/.f64 (*.f64 (cbrt.f64 (fma.f64 x x -3)) (pow.f64 (cbrt.f64 (fma.f64 x x -3)) 2)) 6)
1.1b
(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) 3)
✓0.1b
(/.f64 (-.f64 (*.f64 x x) 3) 6)
Compiler

Compiled 791 to 598 computations (24.4% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.1b
(fma.f64 (/.f64 x 6) x -1/2)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(fma.f64 (/.f64 x 6) x -1/2)
1.0ms
x
@inf
(fma.f64 (/.f64 x 6) x -1/2)
1.0ms
x
@0
(fma.f64 (/.f64 x 6) x -1/2)

rewrite33.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
586×pow1_binary64
553×add-log-exp_binary64
553×log1p-expm1-u_binary64
553×expm1-log1p-u_binary64
544×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11308
214798
Stop Event
1×node limit
Counts
1 → 21
Calls
Call 1
Inputs
(fma.f64 (/.f64 x 6) x -1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1/2 (/.f64 x (/.f64 6 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 x (/.f64 6 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 x (/.f64 6 x)) 1) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 (/.f64 x 6) x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (/.f64 x 6) x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (/.f64 x 6) x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) (cbrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 2)) (cbrt.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) (sqrt.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (/.f64 x (/.f64 6 x)) 3) -1/8) (+.f64 (*.f64 (/.f64 x (/.f64 6 x)) (/.f64 x (/.f64 6 x))) (-.f64 1/4 (*.f64 (/.f64 x (/.f64 6 x)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (/.f64 x (/.f64 6 x)) (/.f64 x (/.f64 6 x))) 1/4) (-.f64 (/.f64 x (/.f64 6 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (/.f64 x 6) x -1/2)))))))

simplify57.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
608×sqr-pow_binary64
441×associate-*l*_binary64
434×unswap-sqr_binary64
281×cube-prod_binary64
276×fabs-mul_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0987
11887
23087
35487
411787
534687
6121187
7210887
8227287
9245687
10266487
11295887
12335187
13382987
14439087
Stop Event
1×node limit
Counts
33 → 26
Calls
Call 1
Inputs
-1/2
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(*.f64 1/6 (pow.f64 x 2))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(*.f64 1/6 (pow.f64 x 2))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
Outputs
-1/2
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)

prune21.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New24226
Fresh224
Picked011
Done101
Total27532
Error
0b
Counts
32 → 5
Alt Table
StatusErrorProgram
10.6b
(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -9) (fma.f64 x x 3)) 6)
✓0.1b
(fma.f64 (/.f64 x 6) x -1/2)
0.4b
(/.f64 (*.f64 (cbrt.f64 (fma.f64 x x -3)) (pow.f64 (cbrt.f64 (fma.f64 x x -3)) 2)) 6)
▶0.1b
(+.f64 -1/2 (/.f64 x (/.f64 6 x)))
0.1b
(fma.f64 1/6 (*.f64 x x) -1/2)
Compiler

Compiled 356 to 267 computations (25% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 x (/.f64 6 x))

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 x (/.f64 6 x))
0.0ms
x
@inf
(/.f64 x (/.f64 6 x))
0.0ms
x
@-inf
(/.f64 x (/.f64 6 x))

rewrite36.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
579×pow1_binary64
546×add-log-exp_binary64
546×log1p-expm1-u_binary64
546×expm1-log1p-u_binary64
535×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11137
215027
Stop Event
1×node limit
Counts
1 → 39
Calls
Call 1
Inputs
(/.f64 x (/.f64 6 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (*.f64 x 1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 x 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (*.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/6))) (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/6))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/6))) 2) (cbrt.f64 (*.f64 x (*.f64 x 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (*.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (*.f64 x 1/6))) (sqrt.f64 (*.f64 x (*.f64 x 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (/.f64 -6 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/6) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/6 (/.f64 x (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 6) (/.f64 (cbrt.f64 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 6) (/.f64 (sqrt.f64 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (/.f64 6 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (/.f64 6 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 6 x) 2))) (/.f64 x (cbrt.f64 (/.f64 6 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (/.f64 6 x) 2))) (cbrt.f64 (*.f64 x (*.f64 x 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (/.f64 6 x) 2))) (/.f64 (sqrt.f64 x) (cbrt.f64 (/.f64 6 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (/.f64 6 x))) (/.f64 x (sqrt.f64 (/.f64 6 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (/.f64 6 x))) (/.f64 (cbrt.f64 x) (sqrt.f64 (/.f64 6 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 1) (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x -6) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x 1/6) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x 1/6) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x 1/6) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x 1/6)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/6))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (*.f64 x 1/6))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 6 (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (/.f64 -6 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 x 1/6)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (/.f64 6 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x 1/6))))))))

simplify56.0ms (3.5%)

Algorithm
1×egg-herbie
Rules
607×sqr-pow_binary64
445×associate-*l*_binary64
434×unswap-sqr_binary64
281×cube-prod_binary64
273×fabs-mul_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
22384
34484
410784
533684
6123784
7211384
8227784
9246184
10266984
11296084
12335384
13383384
14439684
Stop Event
1×node limit
Counts
51 → 41
Calls
Call 1
Inputs
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
Outputs
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))

prune38.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New41041
Fresh033
Picked011
Done011
Total41546
Error
0b
Counts
46 → 5
Alt Table
StatusErrorProgram
10.6b
(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -9) (fma.f64 x x 3)) 6)
✓0.1b
(fma.f64 (/.f64 x 6) x -1/2)
0.4b
(/.f64 (*.f64 (cbrt.f64 (fma.f64 x x -3)) (pow.f64 (cbrt.f64 (fma.f64 x x -3)) 2)) 6)
✓0.1b
(+.f64 -1/2 (/.f64 x (/.f64 6 x)))
▶0.1b
(fma.f64 1/6 (*.f64 x x) -1/2)
Compiler

Compiled 558 to 412 computations (26.2% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.1b
(fma.f64 1/6 (*.f64 x x) -1/2)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(fma.f64 1/6 (*.f64 x x) -1/2)
0.0ms
x
@0
(fma.f64 1/6 (*.f64 x x) -1/2)
0.0ms
x
@inf
(fma.f64 1/6 (*.f64 x x) -1/2)

rewrite33.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
505×pow1_binary64
472×add-log-exp_binary64
472×log1p-expm1-u_binary64
472×expm1-log1p-u_binary64
463×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11228
213048
Stop Event
1×node limit
Counts
1 → 21
Calls
Call 1
Inputs
(fma.f64 1/6 (*.f64 x x) -1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1/2 (*.f64 1/6 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/6 (*.f64 x x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/6 (*.f64 x x)) 1) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/6 (*.f64 x x) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/6 (*.f64 x x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/6 (*.f64 x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/6 (*.f64 x x) -1/2)) (cbrt.f64 (pow.f64 (fma.f64 1/6 (*.f64 x x) -1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 1/6 (*.f64 x x) -1/2) 2)) (cbrt.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/6 (*.f64 x x) -1/2)) (sqrt.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/6 (*.f64 x x)) 3) -1/8) (+.f64 (*.f64 (*.f64 1/6 (*.f64 x x)) (*.f64 1/6 (*.f64 x x))) (-.f64 1/4 (*.f64 (*.f64 1/6 (*.f64 x x)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/6 (*.f64 x x)) (*.f64 1/6 (*.f64 x x))) 1/4) (-.f64 (*.f64 1/6 (*.f64 x x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/6 (*.f64 x x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/6 (*.f64 x x) -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/6 (*.f64 x x) -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/6 (*.f64 x x) -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/6 (*.f64 x x) -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/6 (*.f64 x x) -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))))))

simplify55.0ms (3.5%)

Algorithm
1×egg-herbie
Rules
608×sqr-pow_binary64
441×associate-*l*_binary64
434×unswap-sqr_binary64
281×cube-prod_binary64
276×fabs-mul_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0987
11887
23087
35487
411787
534687
6121187
7210887
8227287
9245687
10266487
11295887
12335187
13382987
14439087
Stop Event
1×node limit
Counts
33 → 26
Calls
Call 1
Inputs
-1/2
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(*.f64 1/6 (pow.f64 x 2))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(*.f64 1/6 (pow.f64 x 2))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
Outputs
-1/2
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)
(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
(fma.f64 1/6 (*.f64 x x) -1/2)

prune18.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New26026
Fresh022
Picked011
Done022
Total26531
Error
0b
Counts
31 → 5
Alt Table
StatusErrorProgram
10.6b
(/.f64 (/.f64 (+.f64 (pow.f64 x 4) -9) (fma.f64 x x 3)) 6)
✓0.1b
(fma.f64 (/.f64 x 6) x -1/2)
0.4b
(/.f64 (*.f64 (cbrt.f64 (fma.f64 x x -3)) (pow.f64 (cbrt.f64 (fma.f64 x x -3)) 2)) 6)
✓0.1b
(+.f64 -1/2 (/.f64 x (/.f64 6 x)))
✓0.1b
(fma.f64 1/6 (*.f64 x x) -1/2)
Compiler

Compiled 312 to 205 computations (34.3% saved)

regimes78.0ms (4.9%)

Accuracy

Total 0.1b remaining (93.2%)

Threshold costs 0.1b (93.2%)

Counts
40 → 1
Compiler

Compiled 383 to 277 computations (27.7% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
1810
Stop Event
1×saturated
Calls
Call 1
Inputs
(+.f64 -1/2 (/.f64 x (/.f64 6 x)))
Outputs
(+.f64 -1/2 (/.f64 x (/.f64 6 x)))

end78.0ms (4.9%)

Stop Event
1×fuel
Compiler

Compiled 67 to 50 computations (25.4% saved)

Profiling

Loading profile data...