Details

analyze235.0ms

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

sample71.0ms

Algorithm

intervals

Results

27.0ms	47×	body	1280	valid
13.0ms	39×	body	640	valid
11.0ms	136×	body	80	valid
7.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	13×	body	80	overflowed
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid
0.0ms	4×	body	80	invalid
0.0ms	1×	body	160	invalid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5443	27

prune7.0ms

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: 27.5b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

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))))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
2.9b	(-.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)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

81×	`exp-neg_binary64` `frac-sub_binary64`
80×	`frac-times_binary64`
61×	`neg-sub0_binary64` `exp-diff_binary64`
40×	`associate-r/_binary64` `associate-l/_binary64`
31×	`flip3--_binary64` `flip--_binary64`
30×	`flip3-+_binary64` `flip-+_binary64`
28×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
20×	`un-div-inv_binary64`
19×	`associate-l_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `add-exp-log_binary64` `difference-of-squares_binary64` `times-frac_binary64` `exp-prod_binary64`
3×	`difference-of-sqr-1_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`

Counts

4 → 176

Calls

4 calls:

14.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
16.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
20.0ms	(-.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)))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
10.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
10.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
34.0ms	(-.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)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5075	6121

prune274.0ms

Filtered

103 candidates to 188 candidates (-82.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	185	3	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	186	3	189

Merged error: 0.4b

Counts

189 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(*.f64 2/3 (pow.f64 x 3))
4.6b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-r_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-l_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:

7.0ms	(*.f64 2/3 (pow.f64 x 3))
8.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(*.f64 2/3 (pow.f64 x 3))
5.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify31.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5491	454

prune52.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Merged error: 0.4b

Counts

54 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 2/3 (pow.f64 x 3))
0.5b	(exp.f64 (log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))))
4.6b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
9.7b	(log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`
9×	`add-log-exp_binary64`
8×	`log-prod_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64`
4×	`unswap-sqr_binary64` `exp-sum_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `log-div_binary64` `exp-prod_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `flip--_binary64`
2×	`diff-log_binary64` `log-pow_binary64` `sqr-pow_binary64` `exp-diff_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 78

Calls

4 calls:

8.0ms	(*.f64 2/3 (pow.f64 x 3))
9.0ms	(exp.f64 (log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))))
8.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
8.0ms	(log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))

series18.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 2/3 (pow.f64 x 3))
4.0ms	(exp.f64 (log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))))
4.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
5.0ms	(log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4850	1074
1	4850	1074

prune97.0ms

Filtered

60 candidates to 90 candidates (-50.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	89	5	94

Merged error: 0.4b

Counts

94 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

4.6b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
6.3b	(log.f64 (pow.f64 (cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))) 2))
10.3b	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
10.3b	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`log-prod_binary64` `cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`unpow-prod-down_binary64`
6×	`add-exp-log_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
3×	`flip3--_binary64` `rem-log-exp_binary64` `flip--_binary64`
2×	`diff-log_binary64` `pow1/3_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `unpow2_binary64` `log-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 65

Calls

4 calls:

8.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
10.0ms	(log.f64 (pow.f64 (cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))) 2))
8.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
8.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
16.0ms	(log.f64 (pow.f64 (cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))) 2))
8.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
9.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))

simplify38.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5016	1373

prune130.0ms

Filtered

64 candidates to 77 candidates (-20.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	77	5	82

Merged error: 0.4b

Counts

82 → 5

regimes118.0ms

Accuracy

96% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.1b

bsearch69.0ms

Steps

Iters	Range		Point
8	15.587615173577765	17996.4874881748	124.28153962528454

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	210	61
1	210	61

end0.0ms

sample2.1s

Algorithm

intervals

Results

967.0ms	1751×	body	1280	valid
427.0ms	1229×	body	640	valid
334.0ms	4083×	body	80	valid
140.0ms	590×	body	320	valid
57.0ms	347×	body	160	valid
16.0ms	205×	body	80	invalid
14.0ms	181×	body	80	overflowed
8.0ms	15×	body	1280	invalid
5.0ms	12×	body	640	invalid
2.0ms	8×	body	320	invalid
0.0ms	2×	body	160	invalid

Details

analyze235.0ms

sample71.0ms

simplify67.0ms

prune7.0ms

localize18.0ms

rewrite65.0ms

series61.0ms

simplify81.0ms

prune274.0ms

localize8.0ms

rewrite16.0ms

series9.0ms

simplify31.0ms

prune52.0ms

localize12.0ms

rewrite36.0ms

series18.0ms

simplify43.0ms

prune97.0ms

localize18.0ms

rewrite36.0ms

series38.0ms

simplify38.0ms

prune130.0ms

regimes118.0ms

bsearch69.0ms

simplify4.0ms

end0.0ms

sample2.1s

Profiling