Details

analyze244.0ms

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

sample77.0ms

Algorithm

intervals

Results

36.0ms	62×	body	1280	valid
16.0ms	46×	body	640	valid
10.0ms	120×	body	80	valid
5.0ms	22×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	4×	body	80	invalid
0.0ms	4×	body	80	overflowed

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4915	27
1	4915	27

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: 32.1b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 1.0 (/.f64 1.0 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))
0.0b	(*.f64 (-.f64 1.0 eps) x)
0.0b	(*.f64 (+.f64 1.0 eps) x)
1.9b	(-.f64 (.f64 (+.f64 1.0 (/.f64 1.0 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x)))) (.f64 (-.f64 (/.f64 1.0 eps) 1.0) (exp.f64 (neg.f64 (.f64 (+.f64 1.0 eps) x)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub_binary64`
76×	`exp-neg_binary64` `frac-times_binary64`
57×	`neg-sub0_binary64` `exp-diff_binary64`
42×	`associate-*l/_binary64`
38×	`associate-*r/_binary64`
31×	`flip3-+_binary64` `flip-+_binary64`
29×	`flip3--_binary64` `flip--_binary64`
19×	`un-div-inv_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
13×	`associate-l_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`distribute-lft-out_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`

Counts

4 → 163

Calls

4 calls:

13.0ms	(.f64 (+.f64 1.0 (/.f64 1.0 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))
7.0ms	(*.f64 (-.f64 1.0 eps) x)
7.0ms	(*.f64 (+.f64 1.0 eps) x)
18.0ms	(-.f64 (.f64 (+.f64 1.0 (/.f64 1.0 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x)))) (.f64 (-.f64 (/.f64 1.0 eps) 1.0) (exp.f64 (neg.f64 (.f64 (+.f64 1.0 eps) x)))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 (+.f64 1.0 (/.f64 1.0 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))
4.0ms	(*.f64 (-.f64 1.0 eps) x)
4.0ms	(*.f64 (+.f64 1.0 eps) x)
103.0ms	(-.f64 (.f64 (+.f64 1.0 (/.f64 1.0 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x)))) (.f64 (-.f64 (/.f64 1.0 eps) 1.0) (exp.f64 (neg.f64 (.f64 (+.f64 1.0 eps) x)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5248	6608

prune251.0ms

Filtered

94 candidates to 175 candidates (-86.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	172	3	175
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	174	3	177

Merged error: 0.2b

Counts

177 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 0.6666666666666667)
5.8b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 0.6666666666666667) 2.0) (.f64 1.0 (*.f64 x x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`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` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 44

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 x 3) 0.6666666666666667)
9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 0.6666666666666667) 2.0) (.f64 1.0 (*.f64 x x)))

series11.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(*.f64 (pow.f64 x 3) 0.6666666666666667)
5.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 0.6666666666666667) 2.0) (.f64 1.0 (*.f64 x x)))

simplify33.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5346	457

prune53.0ms

Filtered

32 candidates to 50 candidates (-56.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	50	3	53

Merged error: 0.2b

Counts

53 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
5.8b	(-.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 0.6666666666666667)) 2.0) (.f64 1.0 (*.f64 x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`add-log-exp_binary64`
8×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `diff-log_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `flip--_binary64` `pow2_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)
11.0ms	(-.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 0.6666666666666667)) 2.0) (.f64 1.0 (*.f64 x x)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
29.0ms	(cbrt.f64 x)
28.0ms	(cbrt.f64 x)
10.0ms	(-.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 0.6666666666666667)) 2.0) (.f64 1.0 (*.f64 x x)))

simplify34.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5286	577

prune89.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	87	3	90

Merged error: 0.2b

Counts

90 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 (neg.f64 (*.f64 (-.f64 1.0 eps) x))))
0.0b	(.f64 (.f64 (+.f64 1.0 (/.f64 1.0 eps)) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x)))))
0.0b	(*.f64 (+.f64 1.0 eps) x)
2.9b	(-.f64 (.f64 (.f64 (+.f64 1.0 (/.f64 1.0 eps)) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))) (.f64 (-.f64 (/.f64 1.0 eps) 1.0) (exp.f64 (neg.f64 (.f64 (+.f64 1.0 eps) x)))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

384×	`frac-times_binary64`
362×	`sqrt-div_binary64`
285×	`exp-neg_binary64`
259×	`neg-sub0_binary64` `exp-diff_binary64`
234×	`frac-sub_binary64`
194×	`associate-*l/_binary64`
132×	`associate-*r/_binary64`
91×	`flip3-+_binary64` `flip-+_binary64`
79×	`flip3--_binary64` `flip--_binary64`
26×	`un-div-inv_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`
7×	`sqrt-pow1_binary64`
6×	`add-log-exp_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
5×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `unswap-sqr_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64`

Counts

4 → 334

Calls

4 calls:

3.0ms	(sqrt.f64 (exp.f64 (neg.f64 (*.f64 (-.f64 1.0 eps) x))))
18.0ms	(.f64 (.f64 (+.f64 1.0 (/.f64 1.0 eps)) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x)))))
6.0ms	(*.f64 (+.f64 1.0 eps) x)
34.0ms	(-.f64 (.f64 (.f64 (+.f64 1.0 (/.f64 1.0 eps)) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))) (.f64 (-.f64 (/.f64 1.0 eps) 1.0) (exp.f64 (neg.f64 (.f64 (+.f64 1.0 eps) x)))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt.f64 (exp.f64 (neg.f64 (*.f64 (-.f64 1.0 eps) x))))
15.0ms	(.f64 (.f64 (+.f64 1.0 (/.f64 1.0 eps)) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x)))))
4.0ms	(*.f64 (+.f64 1.0 eps) x)
99.0ms	(-.f64 (.f64 (.f64 (+.f64 1.0 (/.f64 1.0 eps)) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (-.f64 1.0 eps) x))))) (.f64 (-.f64 (/.f64 1.0 eps) 1.0) (exp.f64 (neg.f64 (.f64 (+.f64 1.0 eps) x)))))

simplify148.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5000	19329

prune341.0ms

Filtered

115 candidates to 346 candidates (-200.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	346	0	346
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	346	3	349

Merged error: 0.2b

Counts

349 → 3

regimes87.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.6b

bsearch83.0ms

Steps

Iters	Range		Point
10	8.333210867680476e-08	231781.61384385402	269.31082505911274

simplify13.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	571	62
1	571	62

end0.0ms

sample2.1s

Algorithm

intervals

Results

962.0ms	1749×	body	1280	valid
444.0ms	1277×	body	640	valid
327.0ms	4050×	body	80	valid
152.0ms	639×	body	320	valid
44.0ms	285×	body	160	valid
19.0ms	202×	body	80	invalid
15.0ms	201×	body	80	overflowed
14.0ms	25×	body	1280	invalid
4.0ms	10×	body	640	invalid
1.0ms	5×	body	320	invalid
1.0ms	3×	body	160	invalid

Details

analyze244.0ms

sample77.0ms

simplify70.0ms

prune11.0ms

localize17.0ms

rewrite54.0ms

series127.0ms

simplify67.0ms

prune251.0ms

localize9.0ms

rewrite17.0ms

series11.0ms

simplify33.0ms

prune53.0ms

localize13.0ms

rewrite22.0ms

series98.0ms

simplify34.0ms

prune89.0ms

localize19.0ms

rewrite100.0ms

series149.0ms

simplify148.0ms

prune341.0ms

regimes87.0ms

bsearch83.0ms

simplify13.0ms

end0.0ms

sample2.1s

Profiling