Details

analyze463.0ms

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

sample31.0ms

Algorithm

intervals

Results

18.0ms	256×	body	128	valid
2.0ms	27×	body	128	invalid
1.0ms	17×	body	128	nan

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4938	36
1	4938	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: 6.7b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.2b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
6.2b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite58.0ms

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:

9.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
16.0ms	(+.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)

series958.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
326.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
191.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
140.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify95.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4930	2143
1	4930	2143

prune196.0ms

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: 5.0b

Counts

109 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
6.2b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite26.0ms

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)
14.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series625.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt.f64 x)
151.0ms	(cbrt.f64 x)
164.0ms	(cbrt.f64 x)
155.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify46.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4934	1155
1	4934	1155

prune154.0ms

Filtered

64 candidates to 74 candidates (-15.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	75	11	86

Merged error: 5.0b

Counts

86 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
4.9b	(pow.f64 x 1/3)
6.2b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite26.0ms

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)
2.0ms	(pow.f64 x 1/3)
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series621.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt.f64 x)
161.0ms	(cbrt.f64 x)
152.0ms	(pow.f64 x 1/3)
157.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5021	1161

prune154.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 5.0b

Counts

92 → 10

localize21.0ms

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 2069265617858471/2251799813685248 x))
0.3b	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (+.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x)))
6.2b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64` `log-prod_binary64` `frac-add_binary64`
22×	`add-cube-cbrt_binary64`
19×	`flip3--_binary64` `flip--_binary64`
18×	`add-log-exp_binary64`
14×	`associate-+l+_binary64` `associate-*l/_binary64`
13×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
12×	`associate-*r/_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` `sub-neg_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` `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 → 125

Calls

4 calls:

9.0ms	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))
17.0ms	(+.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x))
20.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (+.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x)))
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series377.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))
87.0ms	(+.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x))
88.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (+.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 2069265617858471/2251799813685248 x)))
148.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify106.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4926	4611
1	4926	4611

prune248.0ms

Filtered

110 candidates to 137 candidates (-24.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	137	10	147

Merged error: 5.0b

Counts

147 → 10

regimes252.0ms

Accuracy

87.6% (0.3b remaining)

Error of 4.2b against oracle of 3.9b and baseline of 6.1b

bsearch41.0ms

Steps

Iters	Range		Point
8	5472.168381575027	2726829.8304666923	2690112.159335637

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	112	123
1	112	123

end0.0ms

sample927.0ms

Algorithm

intervals

Results

562.0ms	8000×	body	128	valid
84.0ms	1228×	body	128	invalid
47.0ms	705×	body	128	nan

Details

analyze463.0ms

sample31.0ms

simplify112.0ms

prune4.0ms

localize18.0ms

rewrite58.0ms

series958.0ms

simplify95.0ms

prune196.0ms

localize26.0ms

rewrite26.0ms

series625.0ms

simplify46.0ms

prune154.0ms

localize32.0ms

rewrite26.0ms

series621.0ms

simplify65.0ms

prune154.0ms

localize21.0ms

rewrite80.0ms

series377.0ms

simplify106.0ms

prune248.0ms

regimes252.0ms

bsearch41.0ms

simplify4.0ms

end0.0ms

sample927.0ms

Profiling