Details

analyze478.0ms

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

sample32.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
2.0ms	34×	body	80	invalid
1.0ms	20×	body	80	nan

simplify132.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4939	36
1	4939	36

prune4.0ms

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: 5.0b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
4.5b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite42.0ms

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 x 1/2) (log.f64 x))
11.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series490.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
159.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
156.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
78.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify86.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4932	2145
1	4932	2145

prune185.0ms

Filtered

87 candidates to 108 candidates (-24.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	96	12	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	12	109

Merged error: 3.5b

Counts

109 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
4.5b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64` `cbrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/r_binary64` `pow1/3_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
12.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series337.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt.f64 x)
86.0ms	(cbrt.f64 x)
84.0ms	(cbrt.f64 x)
82.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify47.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4929	1155
1	4929	1155

prune133.0ms

Filtered

64 candidates to 74 candidates (-15.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	74	12	86

Merged error: 3.5b

Counts

86 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
4.5b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
5.1b	(pow.f64 x 1/3)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
7×	`add-exp-log_binary64`
6×	`add-cbrt-cube_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `unpow-prod-down_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `pow1/3_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow1/3_binary64`

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
12.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
2.0ms	(pow.f64 x 1/3)

series331.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt.f64 x)
86.0ms	(cbrt.f64 x)
76.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
83.0ms	(pow.f64 x 1/3)

simplify84.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5007	1161

prune144.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	81	12	93

Merged error: 3.5b

Counts

93 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
4.8b	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

rewrite48.0ms

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:

7.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
13.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
7.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
16.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

series488.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
161.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
153.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
77.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

simplify118.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4933	2306
1	4933	2306

prune148.0ms

Filtered

91 candidates to 119 candidates (-30.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	119	12	131

Merged error: 3.5b

Counts

131 → 12

regimes189.0ms

Accuracy

82% (0.3b remaining)

Error of 4.2b against oracle of 3.9b and baseline of 5.8b

bsearch24.0ms

Steps

Iters	Range		Point
5	787.5328570600859	2215.794421642863	2166.3934373709485

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	109	99
1	109	99

end0.0ms

sample920.0ms

Algorithm

intervals

Results

561.0ms	8000×	body	80	valid
88.0ms	1223×	body	80	invalid
44.0ms	709×	body	80	nan

Details

analyze478.0ms

sample32.0ms

simplify132.0ms

prune4.0ms

localize21.0ms

rewrite42.0ms

series490.0ms

simplify86.0ms

prune185.0ms

localize25.0ms

rewrite17.0ms

series337.0ms

simplify47.0ms

prune133.0ms

localize31.0ms

rewrite18.0ms

series331.0ms

simplify84.0ms

prune144.0ms

localize20.0ms

rewrite48.0ms

series488.0ms

simplify118.0ms

prune148.0ms

regimes189.0ms

bsearch24.0ms

simplify5.0ms

end0.0ms

sample920.0ms

Profiling