Details

analyze221.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample70.0ms

Algorithm

intervals

Results

27.0ms	49×	body	1280	valid
17.0ms	46×	body	640	valid
10.0ms	137×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid
1.0ms	1×	body	1280	invalid
0.0ms	6×	body	80	overflowed
0.0ms	1×	body	640	invalid
0.0ms	4×	body	80	invalid
0.0ms	1×	body	320	invalid

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5391	41

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.0b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 1 eps) x)
0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
1.5b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub_binary64`
80×	`exp-neg_binary64` `frac-times_binary64`
60×	`neg-sub0_binary64` `exp-diff_binary64`
42×	`associate-*l/_binary64`
40×	`associate-*r/_binary64`
31×	`flip3-+_binary64` `flip3--_binary64` `add-sqr-sqrt_binary64` `flip--_binary64` `flip-+_binary64`
24×	`*-un-lft-identity_binary64`
23×	`associate-l_binary64`
20×	`un-div-inv_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64`
8×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64` `times-frac_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`distribute-lft-out--_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `diff-log_binary64`

Counts

4 → 180

Calls

4 calls:

6.0ms	(*.f64 (+.f64 1 eps) x)
13.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
17.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
18.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(*.f64 (+.f64 1 eps) x)
29.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
34.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
122.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

simplify144.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4971	9323
1	4971	9323

prune274.0ms

Filtered

104 candidates to 192 candidates (-84.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	2	193

Merged error: 0.7b

Counts

193 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
7.4b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
7×	`add-log-exp_binary64` `add-exp-log_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-r_binary64` `prod-exp_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `difference-of-squares_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 45

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 x 3) 2/3)
8.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

series41.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(*.f64 (pow.f64 x 3) 2/3)
16.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify71.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4859	681
1	4859	681

prune43.0ms

Filtered

32 candidates to 51 candidates (-59.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	49	4	53

Merged error: 0.7b

Counts

53 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
0.1b	(*.f64 (pow.f64 x 3) 2/3)
9.0b	(-.f64 (pow.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2) 3) (pow.f64 x 6))
10.1b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (.f64 x x) (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt_binary64`
60×	`difference-of-squares_binary64`
48×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64` `unpow-prod-down_binary64`
39×	`sqr-pow_binary64`
33×	`add-cube-cbrt_binary64`
24×	`associate-l_binary64`
23×	`cube-prod_binary64`
16×	`add-exp-log_binary64` `associate-/l*_binary64`
10×	`add-cbrt-cube_binary64`
8×	`unswap-sqr_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `prod-exp_binary64`
5×	`distribute-lft-out--_binary64`
4×	`pow1_binary64`
3×	`associate-/r*_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 170

Calls

4 calls:

6.0ms	(*.f64 (pow.f64 x 3) 2/3)
6.0ms	(*.f64 (pow.f64 x 3) 2/3)
14.0ms	(-.f64 (pow.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2) 3) (pow.f64 x 6))
20.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (.f64 x x) (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(*.f64 (pow.f64 x 3) 2/3)
23.0ms	(*.f64 (pow.f64 x 3) 2/3)
51.0ms	(-.f64 (pow.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2) 3) (pow.f64 x 6))
67.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (.f64 x x) (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)))))

simplify150.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5149	9301

prune395.0ms

Filtered

114 candidates to 182 candidates (-59.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	176	6	182
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	179	7	186

Merged error: 0.7b

Counts

186 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (pow.f64 x 6) 5/3)
0.1b	(*.f64 (pow.f64 x 3) 2/3)
0.1b	(*.f64 (pow.f64 x 3) 2/3)
11.0b	(/.f64 (+.f64 (.f64 (pow.f64 x 6) 5/3) (+.f64 8 (.f64 (pow.f64 x 3) 8))) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (.f64 x x) (+.f64 (.f64 (pow.f64 x 3) 2/3) 2)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
31×	`associate-l_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`
12×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
11×	`unswap-sqr_binary64`
9×	`associate-r_binary64` `prod-exp_binary64` `times-frac_binary64`
8×	`cube-prod_binary64`
6×	`sqr-pow_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`pow-to-exp_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-/l_binary64` `pow-exp_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 118

Calls

4 calls:

5.0ms	(*.f64 (pow.f64 x 6) 5/3)
8.0ms	(*.f64 (pow.f64 x 3) 2/3)
6.0ms	(*.f64 (pow.f64 x 3) 2/3)
13.0ms	(/.f64 (+.f64 (.f64 (pow.f64 x 6) 5/3) (+.f64 8 (.f64 (pow.f64 x 3) 8))) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (.f64 x x) (+.f64 (.f64 (pow.f64 x 3) 2/3) 2)))))

series134.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(*.f64 (pow.f64 x 6) 5/3)
27.0ms	(*.f64 (pow.f64 x 3) 2/3)
24.0ms	(*.f64 (pow.f64 x 3) 2/3)
48.0ms	(/.f64 (+.f64 (.f64 (pow.f64 x 6) 5/3) (+.f64 8 (.f64 (pow.f64 x 3) 8))) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (.f64 x x) (+.f64 (.f64 (pow.f64 x 3) 2/3) 2)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5902	3342

prune257.0ms

Filtered

90 candidates to 130 candidates (-44.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	130	7	137

Merged error: 0.7b

Counts

137 → 7

regimes76.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.4b

bsearch88.0ms

Steps

Iters	Range		Point
8	9.6221996165985	24974.799137063197	62.938531400520596

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	177	193
1	177	193

end0.0ms

sample2.1s

Algorithm

intervals

Results

928.0ms	1710×	body	1280	valid
443.0ms	1332×	body	640	valid
313.0ms	4036×	body	80	valid
136.0ms	594×	body	320	valid
49.0ms	328×	body	160	valid
17.0ms	220×	body	80	invalid
11.0ms	149×	body	80	overflowed
7.0ms	13×	body	1280	invalid
6.0ms	17×	body	640	invalid
3.0ms	10×	body	320	invalid
1.0ms	3×	body	160	invalid

Details

analyze221.0ms

sample70.0ms

simplify82.0ms

prune4.0ms

localize17.0ms

rewrite66.0ms

series203.0ms

simplify144.0ms

prune274.0ms

localize8.0ms

rewrite15.0ms

series41.0ms

simplify71.0ms

prune43.0ms

localize18.0ms

rewrite54.0ms

series165.0ms

simplify150.0ms

prune395.0ms

localize19.0ms

rewrite35.0ms

series134.0ms

simplify62.0ms

prune257.0ms

regimes76.0ms

bsearch88.0ms

simplify6.0ms

end0.0ms

sample2.1s

Profiling