Details

analyze1.8s

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

sample2.1s

Algorithm

intervals

Results

2.0s	162×	body	5120	exit
81.0ms	256×	body	80	valid
8.0ms	419×	pre	80	true
0.0ms	1×	body	80	invalid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4652	74
1	4652	74

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

localize57.0ms

Local error

Found 4 expressions with local error:

6.2b	(-.f64 (-.f64 1 z) 1)
6.2b	(-.f64 (-.f64 1 z) 1)
6.2b	(-.f64 (-.f64 1 z) 1)
6.2b	(-.f64 (-.f64 1 z) 1)

rewrite39.0ms

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:

13.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.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)

simplify64.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5347	436

prune402.0ms

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

localize56.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.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)))
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)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
23×	`add-log-exp_binary64`
14×	`frac-add_binary64`
13×	`distribute-lft-out_binary64` `sum-log_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64`
7×	`prod-exp_binary64`
6×	`flip3-+_binary64` `flip-+_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 → 74

Calls

4 calls:

48.0ms	(+.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)))
16.0ms	(.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)))

series33.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(+.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)))
21.0ms	(.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)))

simplify64.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4911	2205
1	4911	2205

prune295.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	80	6	86

Merged error: 0.3b

Counts

86 → 6

localize79.0ms

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 (-.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))))) (-.f64 3 z))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.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)))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

83×	`associate-*r/_binary64`
68×	`frac-times_binary64`
64×	`frac-add_binary64`
60×	`flip3-+_binary64` `flip-+_binary64`
43×	`flip3--_binary64` `flip--_binary64`
35×	`associate-*l/_binary64`
12×	`add-exp-log_binary64`
11×	`pow1_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64`
8×	`prod-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64`
3×	`pow-prod-down_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
2×	`sub-neg_binary64` `associate-+l+_binary64` `sqrt-pow1_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `unswap-sqr_binary64` `pow-sub_binary64` `exp-sum_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 141

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)))
38.0ms	(.f64 (+.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))))) (-.f64 3 z))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
27.0ms	(+.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)))))

series47.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
11.0ms	(.f64 (+.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))))) (-.f64 3 z))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
10.0ms	(+.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)))))

simplify124.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5611	10384

prune4.1s

Filtered

135 candidates to 151 candidates (-11.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	151	6	157

Merged error: 0.2b

Counts

157 → 6

localize82.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 z)) (exp.f64 -15/2))
1.0b	(.f64 (+.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))))) (-.f64 3 z))
1.0b	(sqrt.f64 (*.f64 2 PI.f64))
2.6b	(+.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)))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

83×	`associate-*r/_binary64`
68×	`frac-times_binary64`
64×	`frac-add_binary64`
60×	`flip3-+_binary64` `flip-+_binary64`
43×	`flip3--_binary64` `flip--_binary64`
36×	`associate-*l/_binary64`
15×	`add-cbrt-cube_binary64`
14×	`pow1_binary64`
13×	`add-exp-log_binary64` `prod-exp_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
8×	`associate-r_binary64`
7×	`cbrt-unprod_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`pow-prod-down_binary64`
4×	`associate-l_binary64`
3×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
2×	`sub-neg_binary64` `associate-+l+_binary64` `sqrt-pow1_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `unswap-sqr_binary64` `pow-sub_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 143

Calls

4 calls:

16.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 z)) (exp.f64 -15/2))
35.0ms	(.f64 (+.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))))) (-.f64 3 z))
3.0ms	(sqrt.f64 (*.f64 2 PI.f64))
28.0ms	(+.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)))))

series47.0ms

Counts

4 → 10

Calls

4 calls:

25.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 z)) (exp.f64 -15/2))
11.0ms	(.f64 (+.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))))) (-.f64 3 z))
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))
10.0ms	(+.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)))))

simplify127.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5650	10420

prune3.6s

Filtered

134 candidates to 153 candidates (-14.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	153	6	159

Merged error: 0.2b

Counts

159 → 6

regimes182.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	142	165
1	142	165

end0.0ms

sample50.5s

Algorithm

intervals

Results

47.4s	3921×	body	5120	exit
2.5s	8000×	body	80	valid
225.0ms	12007×	pre	80	true
31.0ms	86×	body	80	invalid

Details

analyze1.8s

sample2.1s

simplify43.0ms

prune12.0ms

localize57.0ms

rewrite39.0ms

series7.0ms

simplify64.0ms

prune402.0ms

localize56.0ms

rewrite90.0ms

series33.0ms

simplify64.0ms

prune295.0ms

localize79.0ms

rewrite94.0ms

series47.0ms

simplify124.0ms

prune4.1s

localize82.0ms

rewrite94.0ms

series47.0ms

simplify127.0ms

prune3.6s

regimes182.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample50.5s

Profiling