Details

analyze490.0ms

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%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

sample33.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
2.0ms	34×	body	80	invalid
2.0ms	32×	body	80	nan

simplify92.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4926	24
1	4926	24

prune5.0ms

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: 6.0b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
5.4b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`
12×	`associate--l+_binary64`
11×	`add-log-exp_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `times-frac_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64` `associate-+l+_binary64`
5×	`associate-l_binary64`
4×	`associate-r_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 96

Calls

4 calls:

8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
12.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series92.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
24.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
19.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
24.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify52.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4891	1411
1	4891	1411

prune156.0ms

Filtered

87 candidates to 108 candidates (-24.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 4.0b

Counts

109 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))
0.2b	(+.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (+.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x)))
0.3b	(+.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x))
5.4b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod_binary64`
30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64` `associate-*l/_binary64`
24×	`frac-add_binary64` `associate-+l+_binary64`
19×	`flip3--_binary64` `flip--_binary64`
18×	`add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-prod_binary64`
9×	`times-frac_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`sum-log_binary64`
6×	`associate-r_binary64`
5×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `associate-+r-_binary64` `log-pow_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `+-commutative_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

9.0ms	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))
22.0ms	(+.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (+.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x)))
13.0ms	(+.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x))
14.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series67.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))
16.0ms	(+.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (+.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x)))
15.0ms	(+.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x))
24.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify76.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4935	3104
1	4935	3104

prune209.0ms

Filtered

116 candidates to 147 candidates (-26.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	147	10	157

Merged error: 4.0b

Counts

157 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (-.f64 x 1/2) (.f64 (log.f64 (cbrt.f64 x)) 2)) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
5.4b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`log-prod_binary64` `associate-+r+_binary64` `cbrt-prod_binary64`
9×	`times-frac_binary64`
8×	`associate-*l/_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow1_binary64` `flip3--_binary64` `frac-add_binary64` `flip--_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1/3_binary64` `flip-+_binary64`
1×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 79

Calls

4 calls:

13.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 (log.f64 (cbrt.f64 x)) 2)) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series143.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 (log.f64 (cbrt.f64 x)) 2)) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
15.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)
26.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify37.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5171	1260

prune131.0ms

Filtered

82 candidates to 91 candidates (-11.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	91	10	101

Merged error: 4.0b

Counts

101 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
5.6b	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`
17×	`associate-r_binary64`
15×	`add-exp-log_binary64`
12×	`associate--l+_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `times-frac_binary64`
9×	`pow1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
8×	`associate-l_binary64`
7×	`associate-+l+_binary64`
5×	`prod-exp_binary64`
4×	`unswap-sqr_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `cbrt-unprod_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`distribute-lft-out_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `log-pow_binary64` `associate-+l-_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
12.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
20.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

series93.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
27.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
15.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
26.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

simplify57.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5171	1520

prune106.0ms

Filtered

91 candidates to 119 candidates (-30.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	118	11	129

Merged error: 4.0b

Counts

129 → 11

regimes451.0ms

Accuracy

83.6% (0.3b remaining)

Error of 4.1b against oracle of 3.7b and baseline of 5.8b

bsearch27.0ms

Steps

Iters	Range		Point
8	1.778075691455011e+36	6.375252967990836e+38	1.4940346439628906e+38

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	99	57
1	99	57

end0.0ms

sample1.1s

Algorithm

intervals

Results

758.0ms	8000×	body	80	valid
90.0ms	1243×	body	80	invalid
45.0ms	738×	body	80	nan

Details

analyze490.0ms

sample33.0ms

simplify92.0ms

prune5.0ms

localize19.0ms

rewrite44.0ms

series92.0ms

simplify52.0ms

prune156.0ms

localize19.0ms

rewrite64.0ms

series67.0ms

simplify76.0ms

prune209.0ms

localize23.0ms

rewrite34.0ms

series143.0ms

simplify37.0ms

prune131.0ms

localize19.0ms

rewrite51.0ms

series93.0ms

simplify57.0ms

prune106.0ms

regimes451.0ms

bsearch27.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling