Details

analyze9.0ms

Algorithm

Search

True	Other	False	Iter
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

sample77.0ms

Algorithm

intervals

Results

57.0ms	256×	body	80	valid
3.0ms	258×	pre	80	true
0.0ms	2×	body	80	invalid

simplify156.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	5680	55

prune28.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 2.6b

Counts

2 → 2

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
0.4b	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0b	(sqrt.f64 PI.f64)
2.5b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_3784`
45×	`add-sqr-sqrt_binary64_3769`
42×	`times-frac_binary64_3779`
36×	`add-cube-cbrt_binary64_3755`
25×	`sqrt-prod_binary64_3763`
22×	`associate-l_binary64_3844`
18×	`frac-add_binary64_3774`
12×	`distribute-lft-out_binary64_3828`
11×	`add-cbrt-cube_binary64_3756`
9×	`add-exp-log_binary64_3748`
8×	`exp-prod_binary64_3738` `associate-r_binary64_3843`
7×	`pow1_binary64_3730` `frac-times_binary64_3776` `associate-*r/_binary64_3845`
6×	`associate-/r*_binary64_3847` `flip-+_binary64_3809` `flip3-+_binary64_3782`
5×	`add-log-exp_binary64_3749`
3×	`div-inv_binary64_3785` `associate-/l*_binary64_3848` `unswap-sqr_binary64_3812` `unpow-prod-down_binary64_3719`
2×	`cbrt-unprod_binary64_3753` `prod-exp_binary64_3735` `cbrt-undiv_binary64_3754` `div-exp_binary64_3737`
1×	`-commutative_binary64_3852` `sqr-pow_binary64_3816` `clear-num_binary64_3787` `frac-2neg_binary64_3777` `associate-l/_binary64_3846` `unpow2_binary64_3727` `rem-exp-log_binary64_3746` `pow-prod-down_binary64_3711` `sqrt-pow1_binary64_3765` `pow1/2_binary64_3720` `distribute-lft-in_binary64_3826` `rem-sqrt-square_binary64_3772` `distribute-rgt-in_binary64_3827`

Counts

4 → 131

Calls

4 calls:

6.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
66.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
2.0ms	(sqrt.f64 PI.f64)
3.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

series622.0ms

Counts

4 → 10

Calls

4 calls:

77.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
502.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.0ms	(sqrt.f64 PI.f64)
42.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

simplify92.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5079	6134

prune860.0ms

Filtered

99 candidates to 141 candidates (-42.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	124	17	141
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	126	17	143

Merged error: 0.7b

Counts

143 → 17

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
0.4b	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

94×	`times-frac_binary64_3779`
86×	`*-un-lft-identity_binary64_3784`
85×	`add-sqr-sqrt_binary64_3769`
66×	`add-cube-cbrt_binary64_3755`
51×	`sqrt-prod_binary64_3763`
46×	`associate-l_binary64_3844`
44×	`unpow-prod-down_binary64_3719`
18×	`frac-add_binary64_3774`
17×	`add-exp-log_binary64_3748`
16×	`sqr-pow_binary64_3816`
12×	`distribute-lft-out_binary64_3828`
11×	`add-cbrt-cube_binary64_3756`
8×	`pow1_binary64_3730` `associate-r_binary64_3843`
7×	`associate-/l_binary64_3848` `frac-times_binary64_3776` `unswap-sqr_binary64_3812` `associate-r/_binary64_3845`
6×	`associate-/r*_binary64_3847` `flip-+_binary64_3809` `div-exp_binary64_3737` `flip3-+_binary64_3782`
4×	`add-log-exp_binary64_3749` `prod-exp_binary64_3735` `pow-pow_binary64_3712`
3×	`exp-prod_binary64_3738` `pow-to-exp_binary64_3709` `div-inv_binary64_3785` `pow-unpow_binary64_3717` `pow-exp_binary64_3708`
2×	`cbrt-unprod_binary64_3753` `cbrt-undiv_binary64_3754`
1×	`-commutative_binary64_3852` `clear-num_binary64_3787` `frac-2neg_binary64_3777` `associate-l/_binary64_3846` `pow-prod-down_binary64_3711` `sqrt-pow1_binary64_3765` `pow1/2_binary64_3720` `distribute-lft-in_binary64_3826` `rem-sqrt-square_binary64_3772` `distribute-rgt-in_binary64_3827`

Counts

4 → 195

Calls

4 calls:

6.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
72.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0ms	(sqrt.f64 PI.f64)
3.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series869.0ms

Counts

4 → 10

Calls

4 calls:

155.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
592.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.0ms	(sqrt.f64 PI.f64)
122.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

simplify125.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4959	9225
1	4959	9225

prune1.4s

Filtered

133 candidates to 205 candidates (-54.1%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	183	22	205
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	191	31	222

Merged error: 0.3b

Counts

222 → 31

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5)))
0.4b	(.f64 (.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (/.f64 1 (sqrt.f64 PI.f64))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_3784`
31×	`frac-add_binary64_3774`
30×	`add-exp-log_binary64_3748`
19×	`prod-exp_binary64_3735` `distribute-lft-out_binary64_3828`
15×	`associate-*r/_binary64_3845`
14×	`frac-times_binary64_3776`
13×	`add-cbrt-cube_binary64_3756`
11×	`flip-+_binary64_3809` `flip3-+_binary64_3782`
10×	`add-sqr-sqrt_binary64_3769`
9×	`add-log-exp_binary64_3749` `add-cube-cbrt_binary64_3755`
8×	`un-div-inv_binary64_3786` `pow1_binary64_3730` `associate-r_binary64_3843`
7×	`times-frac_binary64_3779`
5×	`cbrt-unprod_binary64_3753`
4×	`pow-to-exp_binary64_3709` `pow-pow_binary64_3712` `pow-exp_binary64_3708`
3×	`sqrt-prod_binary64_3763` `exp-prod_binary64_3738` `pow-unpow_binary64_3717` `div-exp_binary64_3737` `unpow-prod-down_binary64_3719` `rec-exp_binary64_3736` `sum-log_binary64_3699`
2×	`associate-*l/_binary64_3846` `div-inv_binary64_3785`
1×	`+-commutative_binary64_3851` `-commutative_binary64_3852` `sqr-pow_binary64_3816` `associate-l*_binary64_3844` `pow-prod-down_binary64_3711` `sqrt-pow1_binary64_3765` `pow1/2_binary64_3720` `distribute-lft-in_binary64_3826` `cbrt-undiv_binary64_3754` `rem-sqrt-square_binary64_3772` `associate-+l+_binary64_3836` `distribute-rgt-in_binary64_3827`

Counts

4 → 109

Calls

4 calls:

42.0ms	(+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5)))
66.0ms	(.f64 (.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (/.f64 1 (sqrt.f64 PI.f64))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0ms	(sqrt.f64 PI.f64)
3.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series918.0ms

Counts

4 → 10

Calls

4 calls:

206.0ms	(+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5)))
597.0ms	(.f64 (.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (/.f64 1 (sqrt.f64 PI.f64))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.0ms	(sqrt.f64 PI.f64)
115.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

simplify115.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5006	6252

prune731.0ms

Filtered

70 candidates to 119 candidates (-70.0%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	7	23	30
Picked	1	0	1
Done	0	0	0
Total	122	28	150

Merged error: 0.2b

Counts

150 → 28

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (/.f64 1 (sqrt.f64 PI.f64))) (+.f64 (exp.f64 (log.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.4b	(exp.f64 (log.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5)))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

31×	`frac-add_binary64_3774`
30×	`add-exp-log_binary64_3748`
26×	`*-un-lft-identity_binary64_3784`
20×	`exp-diff_binary64_3745` `log-div_binary64_3703`
19×	`prod-exp_binary64_3735`
15×	`associate-*r/_binary64_3845`
14×	`frac-times_binary64_3776`
13×	`add-cbrt-cube_binary64_3756`
12×	`add-sqr-sqrt_binary64_3769`
11×	`flip-+_binary64_3809` `flip3-+_binary64_3782` `add-cube-cbrt_binary64_3755`
9×	`pow1_binary64_3730`
8×	`un-div-inv_binary64_3786` `distribute-lft-out_binary64_3828`
7×	`exp-prod_binary64_3738` `log-prod_binary64_3702` `exp-sum_binary64_3743`
5×	`cbrt-unprod_binary64_3753`
4×	`add-log-exp_binary64_3749` `pow-to-exp_binary64_3709` `pow-pow_binary64_3712` `pow-exp_binary64_3708` `associate-r_binary64_3843`
3×	`times-frac_binary64_3779` `sqrt-prod_binary64_3763` `pow-unpow_binary64_3717` `div-exp_binary64_3737` `unpow-prod-down_binary64_3719` `rec-exp_binary64_3736`
2×	`associate-*l/_binary64_3846`
1×	`-commutative_binary64_3852` `sqr-pow_binary64_3816` `associate-l*_binary64_3844` `rem-exp-log_binary64_3746` `pow-prod-down_binary64_3711` `div-inv_binary64_3785` `sqrt-pow1_binary64_3765` `pow1/2_binary64_3720` `distribute-lft-in_binary64_3826` `cbrt-undiv_binary64_3754` `log-pow_binary64_3705` `rem-sqrt-square_binary64_3772` `distribute-rgt-in_binary64_3827`

Counts

4 → 109

Calls

4 calls:

67.0ms	(.f64 (.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (/.f64 1 (sqrt.f64 PI.f64))) (+.f64 (exp.f64 (log.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
42.0ms	(exp.f64 (log.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5)))))
1.0ms	(sqrt.f64 PI.f64)
3.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series903.0ms

Counts

4 → 10

Calls

4 calls:

581.0ms	(.f64 (.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (/.f64 1 (sqrt.f64 PI.f64))) (+.f64 (exp.f64 (log.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
202.0ms	(exp.f64 (log.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5)))))
0.0ms	(sqrt.f64 PI.f64)
118.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

simplify115.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4996	6267
1	4996	6267

prune494.0ms

Filtered

69 candidates to 119 candidates (-72.5%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	1	26	27
Picked	1	0	1
Done	0	0	0
Total	117	30	147

Merged error: 0.2b

Counts

147 → 30

regimes653.0ms

Accuracy

0% (1.0b remaining)

Error of 1.2b against oracle of 0.2b and baseline of 1.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	67
1	32	67

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
88.0ms	8117×	pre	80	true
23.0ms	117×	body	80	invalid

Details

analyze9.0ms

sample77.0ms

simplify156.0ms

prune28.0ms

localize37.0ms

rewrite82.0ms

series622.0ms

simplify92.0ms

prune860.0ms

localize51.0ms

rewrite92.0ms

series869.0ms

simplify125.0ms

prune1.4s

localize46.0ms

rewrite118.0ms

series918.0ms

simplify115.0ms

prune731.0ms

localize50.0ms

rewrite117.0ms

series903.0ms

simplify115.0ms

prune494.0ms

regimes653.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling