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

sample70.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
21.0ms	183×	body	80	nan

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5545	33

prune5.0ms

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: 2.7b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 y (exp.f64 (.f64 2.0 (-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (/.f64 2.0 (*.f64 t 3.0))))))))
0.3b	(/.f64 2.0 (*.f64 t 3.0))
1.1b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (/.f64 2.0 (*.f64 t 3.0)))))
5.4b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub_binary64`
16×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`frac-times_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-*r/_binary64` `times-frac_binary64`
5×	`sub-neg_binary64` `associate-r_binary64`
4×	`flip3-+_binary64` `associate-/r_binary64` `associate--r+_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64` `flip-+_binary64`
3×	`cbrt-unprod_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `exp-sum_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-div_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

15.0ms	(.f64 y (exp.f64 (.f64 2.0 (-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (/.f64 2.0 (*.f64 t 3.0))))))))
5.0ms	(/.f64 2.0 (*.f64 t 3.0))
13.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (/.f64 2.0 (*.f64 t 3.0)))))
8.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series236.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(.f64 y (exp.f64 (.f64 2.0 (-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (/.f64 2.0 (*.f64 t 3.0))))))))
3.0ms	(/.f64 2.0 (*.f64 t 3.0))
62.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (/.f64 2.0 (*.f64 t 3.0)))))
21.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify62.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4999	2679
1	4999	2679

prune182.0ms

Filtered

85 candidates to 105 candidates (-23.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	3	106

Merged error: 0b

Counts

106 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
1.1b	(-.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 5.0 6.0)) (/.f64 2.0 (.f64 t 3.0)))))
2.0b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))

rewrite57.0ms

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)
22.0ms	(-.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 5.0 6.0)) (/.f64 2.0 (.f64 t 3.0)))))
22.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt.f64 t)
18.0ms	(cbrt.f64 t)
70.0ms	(-.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 5.0 6.0)) (/.f64 2.0 (.f64 t 3.0)))))
26.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))

simplify66.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5001	5661

prune354.0ms

Filtered

141 candidates to 178 candidates (-26.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	178	3	181

Merged error: 0b

Counts

181 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 c (+.f64 a 0.8333333333333334))
0.0b	(exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (*.f64 a b))))
0.2b	(.f64 y (exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b)))))
1.5b	(-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`associate-r_binary64`
12×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `exp-sum_binary64` `add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `associate--l+_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`associate-l_binary64`
5×	`sub-neg_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `rem-exp-log_binary64` `flip--_binary64` `exp-to-pow_binary64` `flip-+_binary64` `exp-prod_binary64`

Counts

4 → 76

Calls

4 calls:

6.0ms	(*.f64 c (+.f64 a 0.8333333333333334))
5.0ms	(exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (*.f64 a b))))
8.0ms	(.f64 y (exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b)))))
7.0ms	(-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b))

series63.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(*.f64 c (+.f64 a 0.8333333333333334))
15.0ms	(exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (*.f64 a b))))
32.0ms	(.f64 y (exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b)))))
9.0ms	(-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b))

simplify53.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4997	970
1	4997	970

prune89.0ms

Filtered

61 candidates to 88 candidates (-44.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	88	3	91

Merged error: 0b

Counts

91 → 3

localize31.0ms

Local error

Found 4 expressions with local error:

2.1b	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0))))
3.6b	(.f64 t (.f64 (-.f64 b c) (-.f64 (.f64 (+.f64 a (/.f64 5.0 6.0)) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 2.0 (-.f64 a (/.f64 5.0 6.0))))))
7.2b	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 t (.f64 (-.f64 b c) (-.f64 (.f64 (+.f64 a (/.f64 5.0 6.0)) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 2.0 (-.f64 a (/.f64 5.0 6.0)))))))
28.4b	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 t (.f64 (-.f64 b c) (-.f64 (.f64 (+.f64 a (/.f64 5.0 6.0)) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 2.0 (-.f64 a (/.f64 5.0 6.0))))))) (.f64 t (.f64 (*.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))))

rewrite517.0ms

Algorithm

rewrite-expression-head

Rules

5114×	`associate-*r/_binary64`
1808×	`frac-sub_binary64`
1608×	`flip3--_binary64` `flip--_binary64`
1588×	`frac-times_binary64`
750×	`sqrt-div_binary64`
681×	`flip3-+_binary64` `flip-+_binary64`
500×	`associate-/l/_binary64`
488×	`associate-*l/_binary64`
110×	`sub-div_binary64`
80×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
49×	`sub-neg_binary64`
44×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
36×	`associate--l+_binary64`
30×	`pow1_binary64`
24×	`cbrt-unprod_binary64` `prod-exp_binary64`
20×	`associate--r+_binary64`
18×	`pow-prod-down_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64`
4×	`cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
3×	`associate-/l*_binary64` `times-frac_binary64`
2×	`associate-r_binary64` `associate-/r/_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `diff-log_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 1201

Calls

4 calls:

18.0ms	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0))))
36.0ms	(.f64 t (.f64 (-.f64 b c) (-.f64 (.f64 (+.f64 a (/.f64 5.0 6.0)) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 2.0 (-.f64 a (/.f64 5.0 6.0))))))
63.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 t (.f64 (-.f64 b c) (-.f64 (.f64 (+.f64 a (/.f64 5.0 6.0)) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 2.0 (-.f64 a (/.f64 5.0 6.0)))))))
104.0ms	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 t (.f64 (-.f64 b c) (-.f64 (.f64 (+.f64 a (/.f64 5.0 6.0)) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 2.0 (-.f64 a (/.f64 5.0 6.0))))))) (.f64 t (.f64 (*.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))))

series642.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0))))
61.0ms	(.f64 t (.f64 (-.f64 b c) (-.f64 (.f64 (+.f64 a (/.f64 5.0 6.0)) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 2.0 (-.f64 a (/.f64 5.0 6.0))))))
222.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 t (.f64 (-.f64 b c) (-.f64 (.f64 (+.f64 a (/.f64 5.0 6.0)) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 2.0 (-.f64 a (/.f64 5.0 6.0)))))))
330.0ms	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 t (.f64 (-.f64 b c) (-.f64 (.f64 (+.f64 a (/.f64 5.0 6.0)) (.f64 (.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))) (.f64 2.0 (-.f64 a (/.f64 5.0 6.0))))))) (.f64 t (.f64 (*.f64 t 3.0) (-.f64 a (/.f64 5.0 6.0)))))

simplify634.0ms

Algorithm

egg-herbie

Counts

1213 → 1213

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5202	135924

prune1.2min

Filtered

1187 candidates to 1213 candidates (-2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	1213	0	1213
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	1213	3	1216

Merged error: 0b

Counts

1216 → 3

regimes613.0ms

Accuracy

0% (1.9b remaining)

Error of 2.5b against oracle of 0.6b and baseline of 2.5b

bsearch0.0ms

simplify9.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	436	40
1	436	40

end0.0ms

sample1.9s

Algorithm

intervals

Results

823.0ms	8000×	body	80	valid
512.0ms	5176×	body	80	nan

Details

analyze1.8s

sample70.0ms

simplify36.0ms

prune5.0ms

localize22.0ms

rewrite44.0ms

series236.0ms

simplify62.0ms

prune182.0ms

localize26.0ms

rewrite57.0ms

series131.0ms

simplify66.0ms

prune354.0ms

localize12.0ms

rewrite28.0ms

series63.0ms

simplify53.0ms

prune89.0ms

localize31.0ms

rewrite517.0ms

series642.0ms

simplify634.0ms

prune1.2min

regimes613.0ms

bsearch0.0ms

simplify9.0ms

end0.0ms

sample1.9s

Profiling