Details

analyze1.7s

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

sample1.6s

Algorithm

intervals

Results

1.5s	122×	body	5120	exit
76.0ms	256×	body	80	valid
6.0ms	379×	pre	80	true
0.0ms	1×	body	80	invalid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4805	115
1	4805	115

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.8b

Counts

2 → 2

localize56.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.5b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
44×	`add-log-exp_binary64` `frac-add_binary64`
31×	`distribute-lft-out_binary64` `sum-log_binary64`
10×	`add-exp-log_binary64`
9×	`flip3-+_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
7×	`prod-exp_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`
2×	`pow-prod-down_binary64` `associate-+l+_binary64` `sqrt-pow1_binary64` `+-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `associate-r/_binary64` `associate-l_binary64` `pow-sub_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

91.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
15.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
21.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

series154.0ms

Counts

4 → 10

Calls

4 calls:

46.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
92.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
15.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

simplify121.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4946	7998
1	4946	7998

prune666.0ms

Filtered

69 candidates to 96 candidates (-39.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	87	9	96
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	89	9	98

Merged error: 0.3b

Counts

98 → 9

localize121.0ms

Local error

Found 4 expressions with local error:

2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
12×	`distribute-lft-out_binary64` `sum-log_binary64`
8×	`flip3-+_binary64` `frac-add_binary64` `flip-+_binary64`
4×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `associate-+r+_binary64`

Counts

4 → 68

Calls

4 calls:

22.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
22.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
19.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
16.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
15.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

simplify89.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4923	2204
1	4923	2204

prune2.3s

Filtered

60 candidates to 80 candidates (-33.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	80	9	89

Merged error: 0.3b

Counts

89 → 9

localize60.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(exp.f64 (log.f64 (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))))))))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
44×	`frac-add_binary64`
31×	`distribute-lft-out_binary64`
14×	`exp-diff_binary64` `log-div_binary64`
11×	`exp-sum_binary64`
10×	`pow1_binary64` `log-prod_binary64` `add-exp-log_binary64`
9×	`flip3-+_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
7×	`add-cube-cbrt_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
4×	`associate-r_binary64` `exp-prod_binary64`
3×	`cbrt-unprod_binary64` `sum-log_binary64`
2×	`pow-prod-down_binary64` `sqrt-pow1_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `associate-r/_binary64` `log-pow_binary64` `associate-l_binary64` `rem-exp-log_binary64` `pow-sub_binary64` `+-commutative_binary64` `sqrt-prod_binary64` `associate-+r+_binary64` `pow-exp_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

15.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
104.0ms	(exp.f64 (log.f64 (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))))))))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series159.0ms

Counts

4 → 10

Calls

4 calls:

96.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
48.0ms	(exp.f64 (log.f64 (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))))))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
15.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

simplify133.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4989	7647
1	4989	7647

prune532.0ms

Filtered

71 candidates to 95 candidates (-33.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	95	9	104

Merged error: 0.3b

Counts

104 → 9

localize101.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.5b	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

576×	`frac-times_binary64`
355×	`associate-*l/_binary64`
330×	`flip3--_binary64` `flip--_binary64`
173×	`associate-*r/_binary64`
96×	`flip3-+_binary64` `flip-+_binary64`
51×	`add-exp-log_binary64`
50×	`pow1_binary64` `add-cbrt-cube_binary64`
38×	`prod-exp_binary64`
34×	`cbrt-unprod_binary64`
33×	`pow-prod-down_binary64`
16×	`frac-add_binary64`
6×	`add-log-exp_binary64`
5×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
2×	`associate-+l+_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `pow-sub_binary64` `exp-sum_binary64` `+-commutative_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 345

Calls

4 calls:

20.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
37.0ms	(.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
29.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)))))

series183.0ms

Counts

4 → 10

Calls

4 calls:

100.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
46.0ms	(.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
36.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)))))

simplify365.0ms

Algorithm

egg-herbie

Counts

355 → 355

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4949	33441
1	4949	33441

prune18.4s

Filtered

325 candidates to 355 candidates (-9.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	354	1	355
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	354	10	364

Merged error: 0.3b

Counts

364 → 10

regimes145.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify11.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	206	589
1	206	589

end0.0ms

sample49.6s

Algorithm

intervals

Results

46.6s	3868×	body	5120	exit
2.5s	8000×	body	80	valid
202.0ms	11967×	pre	80	true
32.0ms	99×	body	80	invalid

Details

analyze1.7s

sample1.6s

simplify64.0ms

prune12.0ms

localize56.0ms

rewrite135.0ms

series154.0ms

simplify121.0ms

prune666.0ms

localize121.0ms

rewrite95.0ms

series72.0ms

simplify89.0ms

prune2.3s

localize60.0ms

rewrite149.0ms

series159.0ms

simplify133.0ms

prune532.0ms

localize101.0ms

rewrite128.0ms

series183.0ms

simplify365.0ms

prune18.4s

regimes145.0ms

bsearch0.0ms

simplify11.0ms

end0.0ms

sample49.6s

Profiling