Details

analyze862.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
6.2%	90.4%	3.4%	6
6.2%	90.4%	3.4%	7
6.2%	88.8%	5%	8
7.8%	77.9%	14.3%	9
7.8%	56.5%	35.7%	10
7.8%	56.5%	35.7%	11
8.1%	41.5%	50.3%	12
8.3%	41.4%	50.3%	13
8.4%	40.2%	51.4%	14

sample110.0ms

Algorithm

intervals

Results

30.0ms	456×	body	80	nan
23.0ms	256×	body	80	valid
18.0ms	235×	body	80	invalid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5221	16

prune11.0ms

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: 0.3b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 t 1) (log.f64 a))
0.3b	(*.f64 y (log.f64 z))
0.9b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
1.2b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`log-prod_binary64` `add-exp-log_binary64`
10×	`add-log-exp_binary64` `pow1_binary64` `associate-l_binary64`
8×	`associate-r_binary64`
6×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
5×	`exp-prod_binary64`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `exp-diff_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `associate-r/_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip--_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 96

Calls

4 calls:

10.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
5.0ms	(*.f64 y (log.f64 z))
8.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
12.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series115.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
7.0ms	(*.f64 y (log.f64 z))
40.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
60.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

simplify43.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5352	1150

prune92.0ms

Filtered

76 candidates to 108 candidates (-42.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	102	8	110

Merged error: 0.1b

Counts

110 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 t 1) (log.f64 a))
0.3b	(*.f64 y (log.f64 z))
1.0b	(pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
1.2b	(/.f64 (.f64 x (pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-exp-log_binary64`
16×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`log-prod_binary64`
11×	`pow1_binary64`
10×	`associate-l_binary64`
8×	`associate-r_binary64`
6×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64`
5×	`pow-unpow_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `pow-exp_binary64`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `unpow-prod-down_binary64` `difference-of-squares_binary64` `times-frac_binary64`
2×	`pow-to-exp_binary64` `pow-prod-down_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `unpow-prod-up_binary64` `unswap-sqr_binary64` `pow-sub_binary64` `e-exp-1_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `associate-r/_binary64` `pow-pow_binary64` `difference-of-sqr-1_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 104

Calls

4 calls:

8.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
5.0ms	(*.f64 y (log.f64 z))
7.0ms	(pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
9.0ms	(/.f64 (.f64 x (pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series127.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
9.0ms	(*.f64 y (log.f64 z))
41.0ms	(pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
68.0ms	(/.f64 (.f64 x (pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

simplify32.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5175	1483

prune105.0ms

Filtered

72 candidates to 116 candidates (-61.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	117	7	124

Merged error: 0.0b

Counts

124 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 y (log.f64 z))
1.0b	(pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (/.f64 (.f64 (log.f64 a) (-.f64 (*.f64 t t) 1)) (+.f64 t 1))) b))
1.2b	(/.f64 (.f64 x (pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (/.f64 (.f64 (log.f64 a) (-.f64 (.f64 t t) 1)) (+.f64 t 1))) b))) y)
14.4b	(/.f64 (.f64 (log.f64 a) (-.f64 (.f64 t t) 1)) (+.f64 t 1))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
14×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
7×	`associate-/r*_binary64` `times-frac_binary64` `div-exp_binary64`
6×	`log-prod_binary64` `prod-exp_binary64`
5×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `pow-exp_binary64`
3×	`associate-/l/_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `associate-l*_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `unpow-prod-up_binary64` `associate-/r/_binary64` `clear-num_binary64` `pow-sub_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `e-exp-1_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

5.0ms	(*.f64 y (log.f64 z))
11.0ms	(pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (/.f64 (.f64 (log.f64 a) (-.f64 (*.f64 t t) 1)) (+.f64 t 1))) b))
12.0ms	(/.f64 (.f64 x (pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (/.f64 (.f64 (log.f64 a) (-.f64 (.f64 t t) 1)) (+.f64 t 1))) b))) y)
11.0ms	(/.f64 (.f64 (log.f64 a) (-.f64 (.f64 t t) 1)) (+.f64 t 1))

series254.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 y (log.f64 z))
77.0ms	(pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (/.f64 (.f64 (log.f64 a) (-.f64 (*.f64 t t) 1)) (+.f64 t 1))) b))
147.0ms	(/.f64 (.f64 x (pow.f64 E.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (/.f64 (.f64 (log.f64 a) (-.f64 (.f64 t t) 1)) (+.f64 t 1))) b))) y)
23.0ms	(/.f64 (.f64 (log.f64 a) (-.f64 (.f64 t t) 1)) (+.f64 t 1))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5184	1675

prune83.0ms

Filtered

79 candidates to 112 candidates (-41.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	112	7	119

Merged error: 0.0b

Counts

119 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (-.f64 t 1)))))
0.2b	(pow.f64 a (-.f64 t 1))
0.3b	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (-.f64 t 1))))
1.2b	(/.f64 y (*.f64 x (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (-.f64 t 1))))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

790×	`times-frac_binary64`
397×	`add-sqr-sqrt_binary64`
356×	`*-un-lft-identity_binary64`
353×	`add-cube-cbrt_binary64`
322×	`unpow-prod-down_binary64`
208×	`associate-r_binary64`
112×	`sqr-pow_binary64`
99×	`add-exp-log_binary64`
77×	`div-exp_binary64`
46×	`sub-neg_binary64` `unpow-prod-up_binary64`
32×	`add-cbrt-cube_binary64`
30×	`associate-/r*_binary64`
26×	`prod-exp_binary64`
22×	`pow-to-exp_binary64` `pow-exp_binary64`
18×	`associate-/r/_binary64` `div-inv_binary64`
16×	`pow-sub_binary64`
13×	`cbrt-undiv_binary64` `unswap-sqr_binary64`
10×	`associate-/l*_binary64`
7×	`pow-unpow_binary64` `pow1_binary64`
6×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64`
2×	`associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `pow-pow_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

4 → 573

Calls

4 calls:

56.0ms	(*.f64 x (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (-.f64 t 1)))))
5.0ms	(pow.f64 a (-.f64 t 1))
14.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (-.f64 t 1))))
24.0ms	(/.f64 y (*.f64 x (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (-.f64 t 1))))))

series215.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(*.f64 x (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (-.f64 t 1)))))
11.0ms	(pow.f64 a (-.f64 t 1))
57.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (-.f64 t 1))))
77.0ms	(/.f64 y (*.f64 x (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (-.f64 t 1))))))

simplify100.0ms

Algorithm

egg-herbie

Counts

585 → 585

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5239	11518

prune483.0ms

Filtered

412 candidates to 585 candidates (-42.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	583	2	585
Fresh	1	3	4
Picked	1	0	1
Done	1	1	2
Total	586	6	592

Merged error: 0b

Counts

592 → 6

regimes673.0ms

Accuracy

0% (2.0b remaining)

Error of 2.0b against oracle of 0.0b and baseline of 2.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	18
1	43	18

end0.0ms

sample3.2s

Algorithm

intervals

Results

964.0ms	14409×	body	80	nan
639.0ms	8000×	body	80	valid
569.0ms	7206×	body	80	invalid

Details

analyze862.0ms

sample110.0ms

simplify66.0ms

prune11.0ms

localize15.0ms

rewrite37.0ms

series115.0ms

simplify43.0ms

prune92.0ms

localize17.0ms

rewrite31.0ms

series127.0ms

simplify32.0ms

prune105.0ms

localize22.0ms

rewrite42.0ms

series254.0ms

simplify54.0ms

prune83.0ms

localize17.0ms

rewrite150.0ms

series215.0ms

simplify100.0ms

prune483.0ms

regimes673.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.2s

Profiling