Details

analyze281.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample84.0ms

Algorithm

intervals

Results

39.0ms	78×	body	1280	valid
14.0ms	48×	body	640	valid
10.0ms	31×	body	2560	valid
4.0ms	26×	body	320	valid
3.0ms	62×	body	80	valid
1.0ms	11×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	10	14
1	10	14

prune4.0ms

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: 54.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

1.1b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.4b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
16.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_3142`
6×	`add-sqr-sqrt_binary64_3127`
5×	`pow1_binary64_3088` `add-cube-cbrt_binary64_3113` `add-log-exp_binary64_3107`
4×	`add-exp-log_binary64_3106` `log-prod_binary64_3060`
3×	`sqrt-prod_binary64_3121` `add-cbrt-cube_binary64_3114` `flip-+_binary64_3167` `flip3-+_binary64_3140`
2×	`distribute-lft-out_binary64_3186` `sqrt-div_binary64_3122` `log-div_binary64_3061`
1×	`+-commutative_binary64_3209` `sqrt-pow1_binary64_3123` `log-pow_binary64_3063` `sum-log_binary64_3057` `pow1/2_binary64_3078` `rem-sqrt-square_binary64_3130` `rem-log-exp_binary64_3105`

Counts

3 → 42

Calls

3 calls:

6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series86.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
44.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
17.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify71.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5133	868

prune165.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0.0b

Counts

52 → 4

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
20.7b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_3127`
15×	`associate-l_binary64_3202`
13×	`add-exp-log_binary64_3106`
10×	`associate-r_binary64_3201` `*-un-lft-identity_binary64_3142` `add-cube-cbrt_binary64_3113`
8×	`unpow-prod-down_binary64_3077` `add-log-exp_binary64_3107`
7×	`unswap-sqr_binary64_3170` `add-cbrt-cube_binary64_3114`
6×	`prod-exp_binary64_3093`
4×	`sqr-pow_binary64_3174` `cube-prod_binary64_3115`
3×	`pow1_binary64_3088`
2×	`pow-exp_binary64_3066` `cbrt-unprod_binary64_3111` `pow-to-exp_binary64_3067` `*-commutative_binary64_3210` `diff-log_binary64_3058`
1×	`sum-log_binary64_3057` `sub-neg_binary64_3146` `flip--_binary64_3168` `associate--l+_binary64_3198` `flip3--_binary64_3141` `cube-mult_binary64_3117` `unpow3_binary64_3086`

Counts

3 → 69

Calls

3 calls:

5.0ms	(*.f64 3/40 (pow.f64 x 5))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

series96.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(*.f64 3/40 (pow.f64 x 5))
29.0ms	(*.f64 (pow.f64 x 3) 1/6)
28.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

simplify86.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5102	1008

prune220.0ms

Filtered

50 candidates to 78 candidates (-56.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Merged error: 0.0b

Counts

82 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
21.8b	(+.f64 (.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (+.f64 x (.f64 3/40 (pow.f64 x 5)))) (.f64 (pow.f64 x 6) -1/36))
40.8b	(/.f64 (+.f64 (.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (+.f64 x (.f64 3/40 (pow.f64 x 5)))) (.f64 (pow.f64 x 6) -1/36)) (+.f64 (.f64 (pow.f64 x 3) 1/6) (+.f64 x (.f64 3/40 (pow.f64 x 5)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_3127`
19×	`*-un-lft-identity_binary64_3142` `add-cube-cbrt_binary64_3113`
16×	`add-exp-log_binary64_3106`
15×	`associate-l_binary64_3202`
10×	`add-cbrt-cube_binary64_3114` `associate-r_binary64_3201`
9×	`times-frac_binary64_3137`
8×	`unpow-prod-down_binary64_3077`
7×	`unswap-sqr_binary64_3170`
6×	`add-log-exp_binary64_3107` `prod-exp_binary64_3093`
4×	`pow1_binary64_3088` `sqr-pow_binary64_3174` `cube-prod_binary64_3115`
3×	`associate-/l_binary64_3206` `associate-/r_binary64_3205` `flip-+_binary64_3167` `flip3-+_binary64_3140`
2×	`associate-/l/_binary64_3208` `pow-exp_binary64_3066` `cbrt-unprod_binary64_3111` `pow-to-exp_binary64_3067` `*-commutative_binary64_3210` `associate-/r/_binary64_3207` `associate-+l+_binary64_3194`
1×	`cbrt-undiv_binary64_3112` `div-exp_binary64_3095` `clear-num_binary64_3145` `+-commutative_binary64_3209` `frac-2neg_binary64_3135` `sum-log_binary64_3057` `distribute-rgt-in_binary64_3185` `distribute-lft-in_binary64_3184` `cube-mult_binary64_3117` `unpow3_binary64_3086` `div-inv_binary64_3143`

Counts

4 → 100

Calls

4 calls:

6.0ms	(*.f64 3/40 (pow.f64 x 5))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
15.0ms	(+.f64 (.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (+.f64 x (.f64 3/40 (pow.f64 x 5)))) (.f64 (pow.f64 x 6) -1/36))
18.0ms	(/.f64 (+.f64 (.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (+.f64 x (.f64 3/40 (pow.f64 x 5)))) (.f64 (pow.f64 x 6) -1/36)) (+.f64 (.f64 (pow.f64 x 3) 1/6) (+.f64 x (.f64 3/40 (pow.f64 x 5)))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(*.f64 3/40 (pow.f64 x 5))
28.0ms	(*.f64 (pow.f64 x 3) 1/6)
87.0ms	(+.f64 (.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (+.f64 x (.f64 3/40 (pow.f64 x 5)))) (.f64 (pow.f64 x 6) -1/36))
62.0ms	(/.f64 (+.f64 (.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (+.f64 x (.f64 3/40 (pow.f64 x 5)))) (.f64 (pow.f64 x 6) -1/36)) (+.f64 (.f64 (pow.f64 x 3) 1/6) (+.f64 x (.f64 3/40 (pow.f64 x 5)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5173	3457

prune406.0ms

Filtered

78 candidates to 112 candidates (-43.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	112	5	117

Merged error: 0.0b

Counts

117 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.4b	(/.f64 1/8 (pow.f64 x 3))
14.3b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
17.7b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_3127`
71×	`times-frac_binary64_3137`
68×	`*-un-lft-identity_binary64_3142`
46×	`add-cube-cbrt_binary64_3113`
26×	`unpow-prod-down_binary64_3077`
19×	`associate-/r*_binary64_3205`
15×	`add-exp-log_binary64_3106`
14×	`cube-prod_binary64_3115`
11×	`log-prod_binary64_3060`
10×	`difference-of-squares_binary64_3171` `sqr-pow_binary64_3174`
9×	`add-log-exp_binary64_3107`
8×	`add-cbrt-cube_binary64_3114`
6×	`associate-/l*_binary64_3206` `div-exp_binary64_3095` `distribute-lft-out--_binary64_3187` `frac-sub_binary64_3133`
5×	`pow1_binary64_3088` `log-div_binary64_3061`
4×	`distribute-lft-out_binary64_3186` `cube-mult_binary64_3117` `unpow3_binary64_3086`
2×	`frac-add_binary64_3132` `cbrt-undiv_binary64_3112` `pow-exp_binary64_3066` `clear-num_binary64_3145` `flip-+_binary64_3167` `pow-to-exp_binary64_3067` `frac-2neg_binary64_3135` `flip3-+_binary64_3140` `flip--_binary64_3168` `diff-log_binary64_3058` `flip3--_binary64_3141` `div-inv_binary64_3143`
1×	`log-pow_binary64_3063` `sum-log_binary64_3057` `sub-neg_binary64_3146` `rem-log-exp_binary64_3105` `associate--r+_binary64_3197`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/.f64 1/16 (pow.f64 x 5))
5.0ms	(/.f64 1/8 (pow.f64 x 3))
37.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
35.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

series135.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/.f64 1/16 (pow.f64 x 5))
26.0ms	(/.f64 1/8 (pow.f64 x 3))
40.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
29.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify73.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5089	3605

prune335.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	171	5	176

Merged error: 0.0b

Counts

176 → 5

regimes75.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.4b

bsearch51.0ms

Steps

Iters	Range		Point
9	6357796605034383/144115188075855872	6108725814865727/34359738368	0.9667608709422276
9	-400892148619689/268435456	-2443850143065263/576460752303423488	-1.0832968729492856

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2307×	body	1280	valid
445.0ms	1558×	body	640	valid
287.0ms	825×	body	2560	valid
133.0ms	775×	body	320	valid
94.0ms	2164×	body	80	valid
40.0ms	371×	body	160	valid

Details

analyze281.0ms

sample84.0ms

simplify12.0ms

prune4.0ms

localize10.0ms

rewrite18.0ms

series86.0ms

simplify71.0ms

prune165.0ms

localize14.0ms

rewrite20.0ms

series96.0ms

simplify86.0ms

prune220.0ms

localize24.0ms

rewrite47.0ms

series209.0ms

simplify96.0ms

prune406.0ms

localize25.0ms

rewrite88.0ms

series135.0ms

simplify73.0ms

prune335.0ms

regimes75.0ms

bsearch51.0ms

simplify4.0ms

end0.0ms

sample2.2s

Profiling