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

17.0ms	256×	body	80	valid
3.0ms	37×	body	80	invalid
2.0ms	29×	body	80	nan

simplify133.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4939	36
1	4939	36

prune3.0ms

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: 5.2b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.1b	(-.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) x)

rewrite40.0ms

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:

7.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
11.0ms	(+.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)
12.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series513.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
182.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
165.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
76.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify80.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4932	2145
1	4932	2145

prune179.0ms

Filtered

87 candidates to 108 candidates (-24.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	11	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	11	109

Merged error: 3.5b

Counts

109 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)
0.2b	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x))
4.8b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

16.0ms	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)
16.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x))
12.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series218.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
48.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)
46.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x))
74.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify72.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5452	3068

prune200.0ms

Filtered

96 candidates to 112 candidates (-16.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 3.5b

Counts

123 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.3b	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))
4.8b	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
62×	`*-un-lft-identity_binary64`
60×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
12×	`log-prod_binary64` `associate--l+_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`div-exp_binary64`
7×	`associate-+l+_binary64`
6×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `sum-log_binary64`
1×	`flip3--_binary64` `distribute-lft-out_binary64` `associate-+l-_binary64` `inv-pow_binary64` `+-commutative_binary64` `flip--_binary64` `pow-flip_binary64`

Counts

4 → 151

Calls

4 calls:

11.0ms	(+.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)
14.0ms	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))
11.0ms	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))

series512.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
150.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
79.0ms	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))
123.0ms	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))

simplify119.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4934	4881
1	4934	4881

prune248.0ms

Filtered

120 candidates to 163 candidates (-35.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	164	10	174

Merged error: 2.6b

Counts

174 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
4.8b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite19.0ms

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:

3.0ms	(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)

series335.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(cbrt.f64 x)
83.0ms	(cbrt.f64 x)
97.0ms	(cbrt.f64 x)
75.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4929	1155
1	4929	1155

prune107.0ms

Filtered

64 candidates to 74 candidates (-15.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	74	10	84

Merged error: 2.6b

Counts

84 → 10

regimes206.0ms

Accuracy

53.8% (1.4b remaining)

Error of 4.3b against oracle of 2.9b and baseline of 5.9b

bsearch40.0ms

Steps

Iters	Range		Point
10	1.0648214558492877	21601659046.798336	7497378.413291462

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	100	96
1	100	96

end0.0ms

sample874.0ms

Algorithm

intervals

Results

531.0ms	8000×	body	80	valid
82.0ms	1243×	body	80	invalid
46.0ms	749×	body	80	nan

Details

analyze463.0ms

sample31.0ms

simplify133.0ms

prune3.0ms

localize19.0ms

rewrite40.0ms

series513.0ms

simplify80.0ms

prune179.0ms

localize20.0ms

rewrite55.0ms

series218.0ms

simplify72.0ms

prune200.0ms

localize18.0ms

rewrite49.0ms

series512.0ms

simplify119.0ms

prune248.0ms

localize23.0ms

rewrite19.0ms

series335.0ms

simplify51.0ms

prune107.0ms

regimes206.0ms

bsearch40.0ms

simplify7.0ms

end0.0ms

sample874.0ms

Profiling