Details

Time bar (total: 16.9s)

analyze9.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%25%75%0
0%25%75%1
0%12.5%87.5%2
0%6.3%93.7%3
0%3.1%96.9%4
0%1.6%98.4%5
0%0.8%99.2%6
0%0.4%99.6%7
0%0.2%99.8%8
0.1%0.1%99.8%9
0.1%0%99.9%10
0.1%0%99.9%11
0.1%0%99.9%12
0.1%0%99.9%13
0.1%0%99.9%14
Compiler

Compiled 106 to 71 computations (33% saved)

sample72.0ms (0.4%)

Algorithm
1×intervals
Results
57.0ms256×body128valid
3.0ms256×pre128true
Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify72.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
0551147

prune13.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 2.5b

Counts
2 → 2
Compiler

Compiled 296 to 201 computations (32.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))
0.4b
(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
1.0b
(sqrt.f64 PI.f64)
2.5b
(exp.f64 (*.f64 x x))

rewrite85.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
143×times-frac_binary64
97×add-sqr-sqrt_binary64
88×*-un-lft-identity_binary64
83×add-cube-cbrt_binary64
70×associate-*l*_binary64
43×sqrt-prod_binary64
15×add-cbrt-cube_binary64
13×add-exp-log_binary64
7×pow1_binary64
6×associate-/r*_binary64 add-log-exp_binary64
5×associate-*r*_binary64 div-inv_binary64
4×cbrt-undiv_binary64 unswap-sqr_binary64 div-exp_binary64
3×cbrt-unprod_binary64 distribute-lft-out_binary64 prod-exp_binary64 associate-/l*_binary64
2×flip3-+_binary64 associate-*r/_binary64 flip-+_binary64 frac-times_binary64
1×pow-prod-down_binary64 pow1/2_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 rem-exp-log_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 exp-to-pow_binary64 associate-*l/_binary64 exp-prod_binary64 *-commutative_binary64
Counts
4 → 163
Calls

4 calls:

51.0ms
(*.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))
5.0ms
(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
2.0ms
(exp.f64 (*.f64 x x))
1.0ms
(sqrt.f64 PI.f64)

series257.0ms (1.5%)

Counts
4 → 10
Calls

4 calls:

165.0ms
(*.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))
79.0ms
(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
13.0ms
(exp.f64 (*.f64 x x))
0.0ms
(sqrt.f64 PI.f64)

simplify102.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049626609
149626609

prune4.0s (23.5%)

Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New14924173
Fresh101
Picked101
Done000
Total15124175

Merged error: 0.3b

Counts
175 → 24
Compiler

Compiled 92596 to 56704 computations (38.8% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b
(cbrt.f64 PI.f64)
1.0b
(cbrt.f64 PI.f64)
1.0b
(/.f64 1 (fabs.f64 (cbrt.f64 PI.f64)))
1.1b
(pow.f64 (exp.f64 x) x)

rewrite18.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
17×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
9×times-frac_binary64
7×add-exp-log_binary64
6×pow1_binary64 add-cbrt-cube_binary64 cbrt-prod_binary64
4×add-log-exp_binary64 pow-pow_binary64
3×pow-unpow_binary64 associate-/r*_binary64 unpow-prod-down_binary64 associate-/l*_binary64 exp-prod_binary64
2×pow1/3_binary64
1×pow-to-exp_binary64 cbrt-undiv_binary64 sqr-pow_binary64 clear-num_binary64 inv-pow_binary64 frac-2neg_binary64 rec-exp_binary64 div-inv_binary64 div-exp_binary64 pow-flip_binary64 pow-exp_binary64
Counts
4 → 72
Calls

4 calls:

4.0ms
(pow.f64 (exp.f64 x) x)
3.0ms
(/.f64 1 (fabs.f64 (cbrt.f64 PI.f64)))
1.0ms
(cbrt.f64 PI.f64)
1.0ms
(cbrt.f64 PI.f64)

series33.0ms (0.2%)

Counts
4 → 6
Calls

4 calls:

33.0ms
(pow.f64 (exp.f64 x) x)
0.0ms
(/.f64 1 (fabs.f64 (cbrt.f64 PI.f64)))
0.0ms
(cbrt.f64 PI.f64)
0.0ms
(cbrt.f64 PI.f64)

simplify51.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
05034961

prune624.0ms (3.7%)

Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New72678
Fresh51823
Picked011
Done000
Total7725102

Merged error: 0.3b

Counts
102 → 25
Compiler

Compiled 14632 to 8849 computations (39.5% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)))
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)
1.1b
(pow.f64 (exp.f64 x) x)

rewrite171.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
409×times-frac_binary64
238×add-sqr-sqrt_binary64
205×associate-*r*_binary64
204×sqrt-prod_binary64
203×*-un-lft-identity_binary64
198×add-cube-cbrt_binary64
87×unpow-prod-down_binary64
31×sqr-pow_binary64
19×add-exp-log_binary64
13×add-cbrt-cube_binary64
11×unswap-sqr_binary64
9×pow1_binary64
7×div-exp_binary64
5×associate-*l*_binary64 prod-exp_binary64
4×add-log-exp_binary64 pow-pow_binary64 div-inv_binary64
3×pow-unpow_binary64 cbrt-unprod_binary64 distribute-lft-out_binary64 cbrt-undiv_binary64 exp-prod_binary64
2×pow-to-exp_binary64 flip3-+_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip-+_binary64 frac-times_binary64 pow-exp_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 associate-*r/_binary64 *-commutative_binary64
Counts
4 → 289
Calls

4 calls:

102.0ms
(*.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)))
4.0ms
(pow.f64 (exp.f64 x) x)
1.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)

series323.0ms (1.9%)

Counts
4 → 8
Calls

4 calls:

285.0ms
(*.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)))
38.0ms
(pow.f64 (exp.f64 x) x)
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)

simplify146.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
297 → 297
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
0497014159
1497014159

prune3.5s (20.6%)

Pruning

34 alts after pruning (33 fresh and 1 done)

PrunedKeptTotal
New28314297
Fresh41923
Picked101
Done011
Total28834322

Merged error: 0.2b

Counts
322 → 34
Compiler

Compiled 79607 to 46755 computations (41.3% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)))
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)
1.1b
(pow.f64 (exp.f64 x) x)

rewrite177.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
409×times-frac_binary64
238×add-sqr-sqrt_binary64
205×associate-*r*_binary64
204×sqrt-prod_binary64
203×*-un-lft-identity_binary64
198×add-cube-cbrt_binary64
87×unpow-prod-down_binary64
31×sqr-pow_binary64
19×add-exp-log_binary64
13×add-cbrt-cube_binary64
11×unswap-sqr_binary64
9×pow1_binary64
7×div-exp_binary64
5×associate-*l*_binary64 prod-exp_binary64
4×add-log-exp_binary64 pow-pow_binary64 div-inv_binary64
3×pow-unpow_binary64 cbrt-unprod_binary64 distribute-lft-out_binary64 cbrt-undiv_binary64 exp-prod_binary64
2×pow-to-exp_binary64 flip3-+_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip-+_binary64 frac-times_binary64 pow-exp_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 associate-*r/_binary64 *-commutative_binary64
Counts
4 → 289
Calls

4 calls:

101.0ms
(*.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)))
5.0ms
(pow.f64 (exp.f64 x) x)
1.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)

series306.0ms (1.8%)

Counts
4 → 8
Calls

4 calls:

272.0ms
(*.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)))
33.0ms
(pow.f64 (exp.f64 x) x)
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)

simplify162.0ms (1%)

Algorithm
1×egg-herbie
Counts
297 → 297
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0496914159
1496914159

prune3.6s (21.1%)

Pruning

31 alts after pruning (30 fresh and 1 done)

PrunedKeptTotal
New28512297
Fresh141832
Picked101
Done011
Total30031331

Merged error: 0.2b

Counts
331 → 31
Compiler

Compiled 83445 to 47182 computations (43.5% saved)

regimes143.0ms (0.8%)

Compiler

Compiled 1668 to 1012 computations (39.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03260
13260

end0.0ms (0%)

sample3.0s (17.7%)

Algorithm
1×intervals
Results
1.6s8000×body128valid
103.0ms8129×pre128true
27.0ms129×body128invalid
Compiler

Compiled 1809 to 1109 computations (38.7% saved)

Profiling

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