Details

analyze1.3s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
13.1%	74.3%	12.7%	12
16.1%	70.5%	13.5%	13
18.6%	68%	13.5%	14

sample92.0ms

Algorithm

intervals

Results

36.0ms	59×	body	1280	valid
15.0ms	44×	body	640	valid
8.0ms	109×	body	80	valid
6.0ms	30×	body	320	valid
4.0ms	2×	body	2560	valid
3.0ms	59×	body	80	nan
2.0ms	8×	body	640	nan
2.0ms	12×	body	160	valid
1.0ms	26×	body	80	overflowed
1.0ms	5×	body	320	nan
0.0ms	1×	body	160	nan

simplify232.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (229.0ms)

Iter	Nodes	Cost
0	4988	13
1	4988	13

prune6.0ms

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: 24.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (exp.f64 z))
0.0b	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
1.8b	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
3.4b	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`
9×	`add-log-exp_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`associate-/l*_binary64` `log-div_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-r_binary64` `log-prod_binary64` `associate-l*_binary64` `flip-+_binary64`
2×	`div-sub_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

5.0ms	(*.f64 y (exp.f64 z))
9.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
7.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
8.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 y (exp.f64 z))
41.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
15.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
7.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

simplify44.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5029	1261

prune71.0ms

Filtered

70 candidates to 91 candidates (-30.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Merged error: 5.3b

Counts

92 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

2.1b	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
2.8b	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
6.8b	(.f64 y (.f64 z z))
7.0b	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
23×	`pow1_binary64`
18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`times-frac_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64`
4×	`sub-neg_binary64` `associate-l_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `flip-+_binary64` `associate-+r+_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 92

Calls

4 calls:

14.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
6.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
6.0ms	(.f64 y (.f64 z z))
8.0ms	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)

series66.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
15.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
7.0ms	(.f64 y (.f64 z z))
28.0ms	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)

simplify50.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5365	1512

prune90.0ms

Filtered

67 candidates to 104 candidates (-55.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	98	10	108

Merged error: 5.2b

Counts

108 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 y z) z)
2.1b	(.f64 (.f64 1/2 (.f64 (.f64 y z) z)) (-.f64 1 y))
2.8b	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 (*.f64 y z) z)) (-.f64 1 y)))
7.0b	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 (*.f64 y z) z)) (-.f64 1 y))) t)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
23×	`pow1_binary64`
17×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
13×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`associate-r_binary64` `times-frac_binary64`
6×	`add-log-exp_binary64`
4×	`sub-neg_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `flip-+_binary64` `associate-+r+_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 91

Calls

4 calls:

5.0ms	(.f64 (.f64 y z) z)
13.0ms	(.f64 (.f64 1/2 (.f64 (.f64 y z) z)) (-.f64 1 y))
6.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 (*.f64 y z) z)) (-.f64 1 y)))
9.0ms	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 (*.f64 y z) z)) (-.f64 1 y))) t)

series67.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (.f64 y z) z)
14.0ms	(.f64 (.f64 1/2 (.f64 (.f64 y z) z)) (-.f64 1 y))
17.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 (*.f64 y z) z)) (-.f64 1 y)))
28.0ms	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 (*.f64 y z) z)) (-.f64 1 y))) t)

simplify53.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5003	1506

prune85.0ms

Filtered

64 candidates to 103 candidates (-60.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 5.1b

Counts

113 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

2.1b	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
2.8b	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
6.8b	(.f64 y (.f64 z z))
7.0b	(.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))) (/.f64 1 t))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
25×	`pow1_binary64` `add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
18×	`*-un-lft-identity_binary64`
17×	`prod-exp_binary64`
15×	`cbrt-unprod_binary64`
14×	`pow-prod-down_binary64` `add-cube-cbrt_binary64`
11×	`times-frac_binary64`
7×	`associate-l_binary64`
6×	`add-log-exp_binary64`
4×	`sub-neg_binary64` `unswap-sqr_binary64`
3×	`flip3-+_binary64` `associate-r/_binary64` `flip-+_binary64` `-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `div-exp_binary64` `associate-+r+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`flip3--_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 103

Calls

4 calls:

14.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
6.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
6.0ms	(.f64 y (.f64 z z))
11.0ms	(.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))) (/.f64 1 t))

series68.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
16.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
10.0ms	(.f64 y (.f64 z z))
28.0ms	(.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))) (/.f64 1 t))

simplify67.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5053	1772

prune59.0ms

Filtered

70 candidates to 115 candidates (-64.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	115	10	125

Merged error: 5.1b

Counts

125 → 10

regimes429.0ms

Accuracy

70.8% (4.9b remaining)

Error of 9.1b against oracle of 4.3b and baseline of 21.0b

bsearch24.0ms

Steps

Iters	Range		Point
4	-2.4840099898447955e-07	-1.4025935136632077e-07	-1.6927041196289272e-07

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	340	45
1	340	45

end0.0ms

sample2.7s

Algorithm

intervals

Results

877.0ms	1476×	body	1280	valid
532.0ms	1553×	body	640	valid
253.0ms	3458×	body	80	valid
209.0ms	928×	body	320	valid
97.0ms	72×	body	2560	valid
81.0ms	1573×	body	80	nan
69.0ms	513×	body	160	valid
57.0ms	231×	body	640	nan
46.0ms	851×	body	80	overflowed
41.0ms	118×	body	1280	nan
34.0ms	202×	body	320	nan
11.0ms	107×	body	160	nan
1.0ms	11×	body	80	invalid
0.0ms	1×	body	640	invalid

Details

analyze1.3s

sample92.0ms

simplify232.0ms

prune6.0ms

localize10.0ms

rewrite31.0ms

series69.0ms

simplify44.0ms

prune71.0ms

localize15.0ms

rewrite37.0ms

series66.0ms

simplify50.0ms

prune90.0ms

localize11.0ms

rewrite36.0ms

series67.0ms

simplify53.0ms

prune85.0ms

localize13.0ms

rewrite42.0ms

series68.0ms

simplify67.0ms

prune59.0ms

regimes429.0ms

bsearch24.0ms

simplify7.0ms

end0.0ms

sample2.7s

Profiling