Details

analyze1.8s

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
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

sample62.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
14.0ms	151×	body	80	nan

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4938	29
1	4938	29

prune10.0ms

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: 4.5b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.3b	(/.f64 2 (*.f64 t 3))
2.5b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))
4.0b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`associate-*r/_binary64` `frac-times_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `times-frac_binary64`
5×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
4×	`associate-/r_binary64` `associate--r+_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64` `sqrt-div_binary64`
3×	`sub-neg_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

8.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
5.0ms	(/.f64 2 (*.f64 t 3))
14.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))
8.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series95.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
2.0ms	(/.f64 2 (*.f64 t 3))
55.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))
23.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify59.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4943	1958
1	4943	1958

prune136.0ms

Filtered

87 candidates to 110 candidates (-26.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Merged error: 0.0b

Counts

111 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
2.4b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
2.5b	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (.f64 t 3)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
60×	`frac-sub_binary64`
58×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
46×	`associate-r_binary64`
39×	`frac-times_binary64`
35×	`add-cube-cbrt_binary64`
31×	`cbrt-prod_binary64`
28×	`sqrt-prod_binary64`
27×	`associate-*r/_binary64`
25×	`flip3--_binary64` `add-exp-log_binary64` `flip--_binary64`
21×	`associate-*l/_binary64`
18×	`add-cbrt-cube_binary64`
10×	`unswap-sqr_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out_binary64`
4×	`associate--r+_binary64`
3×	`sub-neg_binary64`
2×	`pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-inv_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `*-commutative_binary64`

Counts

4 → 166

Calls

4 calls:

1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)
26.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
21.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (.f64 t 3)))))

series117.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt.f64 t)
14.0ms	(cbrt.f64 t)
29.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
60.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (.f64 t 3)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5027	5143

prune256.0ms

Filtered

141 candidates to 178 candidates (-26.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	178	4	182

Merged error: 0.0b

Counts

182 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2/3 t)
4.0b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
4.2b	(log.f64 (exp.f64 (/.f64 2/3 t)))
4.4b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (log.f64 (exp.f64 (/.f64 2/3 t))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
14×	`log-pow_binary64`
13×	`exp-prod_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`frac-sub_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
5×	`pow1_binary64`
4×	`associate--r+_binary64` `associate-r/_binary64` `associate-/l_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `log-prod_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `prod-exp_binary64` `flip-+_binary64`

Counts

4 → 98

Calls

4 calls:

4.0ms	(/.f64 2/3 t)
8.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
5.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
14.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (log.f64 (exp.f64 (/.f64 2/3 t))))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/.f64 2/3 t)
19.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
2.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
56.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (log.f64 (exp.f64 (/.f64 2/3 t))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4953	1504
1	4953	1504

prune106.0ms

Filtered

88 candidates to 110 candidates (-25.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Merged error: 0.0b

Counts

114 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x (.f64 y (exp.f64 (.f64 2 (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))))))
0.0b	(exp.f64 (.f64 2 (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
0.1b	(*.f64 c (+.f64 a 5/6))
1.7b	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
6×	`pow1_binary64` `exp-sum_binary64` `associate--l+_binary64`
4×	`associate-r_binary64`
3×	`associate-/r_binary64` `sub-neg_binary64` `associate-l_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(/.f64 x (+.f64 x (.f64 y (exp.f64 (.f64 2 (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))))))
5.0ms	(exp.f64 (.f64 2 (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
7.0ms	(*.f64 c (+.f64 a 5/6))
7.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

series70.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/.f64 x (+.f64 x (.f64 y (exp.f64 (.f64 2 (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))))))
13.0ms	(exp.f64 (.f64 2 (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
5.0ms	(*.f64 c (+.f64 a 5/6))
9.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

simplify65.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5200	1353

prune79.0ms

Filtered

65 candidates to 93 candidates (-43.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	93	4	97

Merged error: 0.0b

Counts

97 → 4

regimes543.0ms

Accuracy

-9.9% (2.4b remaining)

Error of 3.0b against oracle of 0.6b and baseline of 2.7b

bsearch163.0ms

Steps

Iters	Range		Point
7	1.2531950689923091e-281	8.845490409127154e-280	1.0664574295631435e-280
9	-1.812774406464577e+41	-1.1723060818974497e+36	-5.158297158568585e+36

simplify24.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	871	102
1	871	102

end0.0ms

sample1.8s

Algorithm

intervals

Results

769.0ms	8000×	body	80	valid
471.0ms	5026×	body	80	nan

Details

analyze1.8s

sample62.0ms

simplify27.0ms

prune10.0ms

localize22.0ms

rewrite40.0ms

series95.0ms

simplify59.0ms

prune136.0ms

localize26.0ms

rewrite60.0ms

series117.0ms

simplify49.0ms

prune256.0ms

localize27.0ms

rewrite34.0ms

series80.0ms

simplify49.0ms

prune106.0ms

localize15.0ms

rewrite25.0ms

series70.0ms

simplify65.0ms

prune79.0ms

regimes543.0ms

bsearch163.0ms

simplify24.0ms

end0.0ms

sample1.8s

Profiling