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

sample1.4s

Algorithm

intervals

Results

1.3s	112×	body	5120	exit
76.0ms	256×	body	80	valid
6.0ms	370×	pre	80	true
1.0ms	2×	body	80	invalid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4652	74
1	4652	74

prune11.0ms

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

localize59.0ms

Local error

Found 4 expressions with local error:

5.8b	(-.f64 (-.f64 1 z) 1)
5.8b	(-.f64 (-.f64 1 z) 1)
5.8b	(-.f64 (-.f64 1 z) 1)
5.8b	(-.f64 (-.f64 1 z) 1)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
24×	`add-log-exp_binary64`
20×	`add-sqr-sqrt_binary64`
12×	`diff-log_binary64` `distribute-lft-out--_binary64`
8×	`sub-neg_binary64` `difference-of-squares_binary64`
4×	`pow1_binary64` `flip3--_binary64` `associate--l-_binary64` `add-cube-cbrt_binary64` `difference-of-sqr-1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 76

Calls

4 calls:

8.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)

series7.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(-.f64 (-.f64 1 z) 1)

simplify68.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5347	436

prune369.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	88	2	90

Merged error: 1.8b

Counts

90 → 2

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 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))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
18×	`add-log-exp_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64` `sum-log_binary64`
8×	`frac-add_binary64`
7×	`prod-exp_binary64`
5×	`flip3-+_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `flip-+_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 → 70

Calls

4 calls:

32.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
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)))
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)))

series32.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
22.0ms	(.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))
4.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

simplify84.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4945	1712
1	4945	1712

prune224.0ms

Filtered

61 candidates to 80 candidates (-31.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	77	5	82

Merged error: 1.1b

Counts

82 → 5

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
1.0b	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 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))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
27×	`add-log-exp_binary64`
16×	`distribute-lft-out_binary64` `sum-log_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64`
8×	`frac-add_binary64`
7×	`prod-exp_binary64`
5×	`flip3-+_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `flip-+_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 → 74

Calls

4 calls:

57.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
42.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 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)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series39.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
6.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
25.0ms	(.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))

simplify42.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4947	2151
1	4947	2151

prune224.0ms

Filtered

58 candidates to 84 candidates (-44.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 0.3b

Counts

89 → 6

localize62.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (/.f64 848079078717083/1099511627776 (-.f64 3 z)) (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 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	(exp.f64 (log.f64 (+.f64 (+.f64 (/.f64 848079078717083/1099511627776 (-.f64 3 z)) (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
16×	`distribute-lft-out_binary64`
13×	`add-log-exp_binary64`
10×	`pow1_binary64` `add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`frac-add_binary64` `exp-sum_binary64`
7×	`log-prod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
6×	`exp-diff_binary64` `log-div_binary64` `sum-log_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-r_binary64` `exp-prod_binary64`
3×	`cbrt-unprod_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 → 76

Calls

4 calls:

48.0ms	(+.f64 (/.f64 848079078717083/1099511627776 (-.f64 3 z)) (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))))
17.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
60.0ms	(exp.f64 (log.f64 (+.f64 (+.f64 (/.f64 848079078717083/1099511627776 (-.f64 3 z)) (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series37.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(+.f64 (/.f64 848079078717083/1099511627776 (-.f64 3 z)) (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))))
22.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
8.0ms	(exp.f64 (log.f64 (+.f64 (+.f64 (/.f64 848079078717083/1099511627776 (-.f64 3 z)) (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify49.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5424	2290

prune218.0ms

Filtered

58 candidates to 86 candidates (-48.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 0.3b

Counts

92 → 6

regimes52.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	104	75
1	104	75

end0.0ms

sample48.8s

Algorithm

intervals

Results

45.7s	3816×	body	5120	exit
2.5s	8000×	body	80	valid
207.0ms	11913×	pre	80	true
33.0ms	97×	body	80	invalid

Details

analyze1.7s

sample1.4s

simplify41.0ms

prune11.0ms

localize59.0ms

rewrite36.0ms

series7.0ms

simplify68.0ms

prune369.0ms

localize53.0ms

rewrite78.0ms

series32.0ms

simplify84.0ms

prune224.0ms

localize52.0ms

rewrite119.0ms

series39.0ms

simplify42.0ms

prune224.0ms

localize62.0ms

rewrite130.0ms

series37.0ms

simplify49.0ms

prune218.0ms

regimes52.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample48.8s

Profiling