Details

analyze474.0ms

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

sample35.0ms

Algorithm

intervals

Results

21.0ms	256×	body	128	valid
3.0ms	36×	body	128	invalid
1.0ms	18×	body	128	nan

simplify119.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (111.0ms)

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: 5.0b

Counts

2 → 1

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)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
4.6b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite56.0ms

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:

12.0ms	(+.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)
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)

series952.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
312.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
181.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
142.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify88.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4930	2143
1	4930	2143

prune183.0ms

Filtered

86 candidates to 108 candidates (-25.6%)

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: 3.0b

Counts

109 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
4.6b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite25.0ms

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

series618.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt.f64 x)
156.0ms	(cbrt.f64 x)
151.0ms	(cbrt.f64 x)
147.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify40.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4934	1155
1	4934	1155

prune139.0ms

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: 3.0b

Counts

86 → 12

localize22.0ms

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)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
4.7b	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

rewrite58.0ms

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`
13×	`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`
4×	`unswap-sqr_binary64` `prod-exp_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` `flip--_binary64` `frac-times_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`distribute-lft-out_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` `div-exp_binary64` `+-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

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)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
18.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

series941.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
299.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
189.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
143.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

simplify73.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5034	2276

prune163.0ms

Filtered

89 candidates to 118 candidates (-32.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	118	12	130

Merged error: 3.0b

Counts

130 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.3b	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))
4.5b	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
64×	`*-un-lft-identity_binary64`
62×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`
16×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
12×	`log-prod_binary64`
11×	`associate-/r/_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64` `div-inv_binary64` `associate--l+_binary64`
5×	`flip3-+_binary64` `associate-l_binary64` `div-exp_binary64` `flip-+_binary64`
4×	`associate-r_binary64` `cbrt-undiv_binary64`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 157

Calls

4 calls:

8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
16.0ms	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))
13.0ms	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))

series874.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
191.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
151.0ms	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))
235.0ms	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))

simplify97.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4954	4816
1	4954	4816

prune245.0ms

Filtered

121 candidates to 169 candidates (-39.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	169	12	181

Merged error: 2.6b

Counts

181 → 12

regimes244.0ms

Accuracy

60.5% (1.3b remaining)

Error of 4.2b against oracle of 2.9b and baseline of 6.2b

bsearch21.0ms

Steps

Iters	Range		Point
4	5.057213794875918e+37	7.410852709745846e+37	5.130765010965603e+37

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	96
1	100	96

end0.0ms

sample1.1s

Algorithm

intervals

Results

768.0ms	8000×	body	128	valid
90.0ms	1247×	body	128	invalid
50.0ms	710×	body	128	nan

Details

analyze474.0ms

sample35.0ms

simplify119.0ms

prune4.0ms

localize18.0ms

rewrite56.0ms

series952.0ms

simplify88.0ms

prune183.0ms

localize27.0ms

rewrite25.0ms

series618.0ms

simplify40.0ms

prune139.0ms

localize22.0ms

rewrite58.0ms

series941.0ms

simplify73.0ms

prune163.0ms

localize22.0ms

rewrite65.0ms

series874.0ms

simplify97.0ms

prune245.0ms

regimes244.0ms

bsearch21.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling