Details

analyze1.1s

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

sample76.0ms

Algorithm

intervals

Results

26.0ms	59×	body	1024	valid
12.0ms	49×	body	512	valid
9.0ms	120×	body	128	valid
5.0ms	3×	body	2048	valid
4.0ms	25×	body	256	valid
2.0ms	7×	body	1024	nan
2.0ms	10×	body	512	nan
2.0ms	36×	body	128	nan
1.0ms	21×	body	128	overflowed
1.0ms	6×	body	256	nan

simplify291.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (284.0ms)

Iter	Nodes	Cost
0	5254	20

prune2.0ms

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: 26.9b

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))))
4.1b	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

rewrite40.0ms

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:

9.0ms	(*.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))))
7.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(*.f64 y (exp.f64 z))
397.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
124.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
49.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

simplify79.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4974	1971
1	4974	1971

prune99.0ms

Filtered

70 candidates to 91 candidates (-30.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	7	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Merged error: 4.8b

Counts

92 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 z (.f64 1/2 (.f64 z z)))
0.1b	(/.f64 (log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))) t)
3.1b	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
5.3b	(log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))))

rewrite28.0ms

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-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
6×	`add-log-exp_binary64`
5×	`log-pow_binary64`
4×	`flip3-+_binary64` `associate-/l*_binary64` `log-div_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `log-prod_binary64` `associate-l*_binary64`
2×	`associate-*r/_binary64` `div-sub_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

4.0ms	(+.f64 z (.f64 1/2 (.f64 z z)))
6.0ms	(/.f64 (log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))) t)
6.0ms	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
3.0ms	(log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))))

series612.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+.f64 z (.f64 1/2 (.f64 z z)))
306.0ms	(/.f64 (log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))) t)
107.0ms	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
127.0ms	(log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4908	2283
1	4908	2283

prune98.0ms

Filtered

66 candidates to 92 candidates (-39.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	90	9	99

Merged error: 4.8b

Counts

99 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

3.1b	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
3.1b	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
4.3b	(log.f64 (sqrt.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))))
4.3b	(log.f64 (sqrt.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `pow1_binary64` `log-prod_binary64` `add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-r_binary64` `log-pow_binary64` `associate-l_binary64` `sqrt-prod_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `associate-*r/_binary64` `log-div_binary64` `flip-+_binary64` `sqrt-div_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
6.0ms	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
6.0ms	(log.f64 (sqrt.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))))
4.0ms	(log.f64 (sqrt.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

109.0ms	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
107.0ms	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
723.0ms	(log.f64 (sqrt.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))))
747.0ms	(log.f64 (sqrt.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5494	2106

prune136.0ms

Filtered

66 candidates to 94 candidates (-42.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 4.8b

Counts

103 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 t (log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))))
0.1b	(/.f64 1 (/.f64 t (log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))))))
3.1b	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
5.3b	(log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac_binary64`
67×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
24×	`pow1_binary64`
20×	`associate-/r*_binary64`
17×	`log-pow_binary64` `add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
3×	`associate-r_binary64` `log-prod_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `log-div_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `prod-exp_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 153

Calls

4 calls:

3.0ms	(/.f64 t (log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))))
7.0ms	(/.f64 1 (/.f64 t (log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))))))
6.0ms	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
3.0ms	(log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

575.0ms	(/.f64 t (log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z)))))))
224.0ms	(/.f64 1 (/.f64 t (log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))))))
97.0ms	(.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))
125.0ms	(log.f64 (+.f64 1 (.f64 y (+.f64 z (.f64 1/2 (*.f64 z z))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5021	5268

prune151.0ms

Filtered

103 candidates to 165 candidates (-60.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	163	12	175

Merged error: 4.2b

Counts

175 → 12

regimes256.0ms

Accuracy

39.5% (5.4b remaining)

Error of 9.3b against oracle of 3.9b and baseline of 12.9b

bsearch118.0ms

Steps

Iters	Range		Point
8	-1.434675238375483e-265	-1.8900335438106879e-268	-1.9127395416232138e-268
9	-0.000324708090962438	-3.931580038864788e-12	-0.00010467878307697763

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	155	87
1	155	87

end0.0ms

sample2.4s

Algorithm

intervals

Results

830.0ms	1813×	body	1024	valid
349.0ms	1400×	body	512	valid
286.0ms	3787×	body	128	valid
269.0ms	277×	body	2048	valid
107.0ms	723×	body	256	valid
79.0ms	1562×	body	128	nan
51.0ms	174×	body	1024	nan
48.0ms	267×	body	512	nan
47.0ms	828×	body	128	overflowed
18.0ms	164×	body	256	nan
1.0ms	24×	body	128	invalid
1.0ms	2×	body	1024	invalid

Details

analyze1.1s

sample76.0ms

simplify291.0ms

prune2.0ms

localize10.0ms

rewrite40.0ms

series605.0ms

simplify79.0ms

prune99.0ms

localize12.0ms

rewrite28.0ms

series612.0ms

simplify80.0ms

prune98.0ms

localize14.0ms

rewrite32.0ms

series1.7s

simplify73.0ms

prune136.0ms

localize14.0ms

rewrite38.0ms

series1.0s

simplify71.0ms

prune151.0ms

regimes256.0ms

bsearch118.0ms

simplify4.0ms

end0.0ms

sample2.4s

Profiling