Details

analyze1.8s (3.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115
0	1	1
1	1	1

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

Compiler

Compiled 126 to 112 computations (11.1% saved)

sample1.1s (1.9%)

Algorithm

1×

intervals

Results

1.0s	92×	body	8192	exit
75.0ms	256×	body	128	valid
5.0ms	349×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify49.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune12.0ms (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

Error

1.8b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize56.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.9b	(-.f64 (-.f64 1 z) 1)
5.9b	(-.f64 (-.f64 1 z) 1)
5.9b	(-.f64 (-.f64 1 z) 1)
5.9b	(-.f64 (-.f64 1 z) 1)

rewrite1.1s (1.8%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

36×	`*-un-lft-identity_binary64_2465`
28×	`add-sqr-sqrt_binary64_2487`
24×	`add-log-exp_binary64_2504` `cancel-sign-sub-inv_binary64_2431`
16×	`associate--l+_binary64_2402`
12×	`diff-log_binary64_2557` `add-cube-cbrt_binary64_2500` `distribute-lft-out--_binary64_2417`
8×	`sub-neg_binary64_2458` `difference-of-squares_binary64_2434`
4×	`pow1_binary64_2526` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `flip3--_binary64_2469` `flip--_binary64_2440` `difference-of-sqr-1_binary64_2435` `associate--l-_binary64_2403`

Counts

4 → 100

Calls

4 calls:

15.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 12896 to 10998 computations (14.7% saved)

series213.0ms (0.4%)

Error

1.8b

Counts

4 → 12

Calls

4 calls:

42.0ms	(-.f64 (-.f64 1 z) 1)
39.0ms	(-.f64 (-.f64 1 z) 1)
37.0ms	(-.f64 (-.f64 1 z) 1)
37.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 4356 to 3833 computations (12% saved)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5392	704

prune1.1s (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	112	2	114

Error

1.8b

Counts

114 → 2

Compiler

Compiled 13990 to 11821 computations (15.5% saved)

localize55.0ms (0.1%)

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)))

rewrite460.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

19×	`*-un-lft-identity_binary64_2465`
18×	`add-log-exp_binary64_2504`
10×	`add-exp-log_binary64_2503`
9×	`sum-log_binary64_2556` `pow1_binary64_2526` `add-cbrt-cube_binary64_2501` `distribute-lft-out_binary64_2416`
8×	`frac-add_binary64_2473`
7×	`prod-exp_binary64_2514`
5×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487` `flip3-+_binary64_2468` `flip-+_binary64_2439`
4×	`associate-r_binary64_2405`
3×	`cbrt-unprod_binary64_2498`
2×	`associate-+l+_binary64_2398` `+-commutative_binary64_2395` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483`
1×	`pow1/2_binary64_2545` `sqrt-prod_binary64_2481` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `pow-sub_binary64_2541` `associate-r/_binary64_2407` `associate-l/_binary64_2408` `associate-l_binary64_2406` `exp-sum_binary64_2511` `*-commutative_binary64_2396`

Counts

4 → 70

Calls

4 calls:

39.0ms	(+.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 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 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))

Compiler

Compiled 6200 to 4800 computations (22.6% saved)

series350.0ms (0.6%)

Error

1.1b

Counts

4 → 20

Calls

4 calls:

187.0ms	(.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	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
38.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3676 to 2954 computations (19.6% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5563	2799

prune445.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	86	6	92

Error

1.1b

Counts

92 → 6

Compiler

Compiled 7892 to 6090 computations (22.8% saved)

localize55.0ms (0.1%)

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))

rewrite576.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

28×	`*-un-lft-identity_binary64_2465`
27×	`add-log-exp_binary64_2504`
16×	`sum-log_binary64_2556` `distribute-lft-out_binary64_2416`
10×	`add-exp-log_binary64_2503`
9×	`pow1_binary64_2526` `add-cbrt-cube_binary64_2501`
8×	`frac-add_binary64_2473`
7×	`prod-exp_binary64_2514`
5×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487` `flip3-+_binary64_2468` `flip-+_binary64_2439`
4×	`associate-r_binary64_2405`
3×	`cbrt-unprod_binary64_2498`
2×	`pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483` `associate-+l+_binary64_2398` `+-commutative_binary64_2395`
1×	`pow1/2_binary64_2545` `sqrt-prod_binary64_2481` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `pow-sub_binary64_2541` `associate-r/_binary64_2407` `associate-l/_binary64_2408` `associate-l_binary64_2406` `exp-sum_binary64_2511` `*-commutative_binary64_2396`

Counts

4 → 74

Calls

4 calls:

69.0ms	(+.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)))
55.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 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)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6817 to 5294 computations (22.3% saved)

series395.0ms (0.7%)

Error

1.1b

Counts

4 → 26

Calls

4 calls:

187.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
69.0ms	(+.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)))
48.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 4164 to 3328 computations (20.1% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4909	3662
1	4909	3662

prune484.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	101	5	106

Error

0.2b

Counts

106 → 5

Compiler

Compiled 8549 to 6577 computations (23.1% saved)

localize52.0ms (0.1%)

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

rewrite607.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

29×	`*-un-lft-identity_binary64_2465`
27×	`add-log-exp_binary64_2504`
18×	`add-exp-log_binary64_2503`
16×	`prod-exp_binary64_2514` `sum-log_binary64_2556` `distribute-lft-out_binary64_2416`
13×	`add-cbrt-cube_binary64_2501`
8×	`frac-add_binary64_2473`
7×	`pow1_binary64_2526` `add-sqr-sqrt_binary64_2487`
6×	`add-cube-cbrt_binary64_2500` `cbrt-unprod_binary64_2498`
5×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
4×	`associate-r_binary64_2405`
3×	`sqrt-prod_binary64_2481`
2×	`pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `associate-+l+_binary64_2398` `+-commutative_binary64_2395`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `pow-prod-down_binary64_2536` `pow-sub_binary64_2541` `associate-r/_binary64_2407` `associate-l/_binary64_2408` `associate-l_binary64_2406` `exp-sum_binary64_2511` `*-commutative_binary64_2396`

Counts

4 → 80

Calls

4 calls:

66.0ms	(+.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)))
47.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
19.0ms	(.f64 (.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 7401 to 5653 computations (23.6% saved)

series394.0ms (0.7%)

Error

0.2b

Counts

4 → 26

Calls

4 calls:

185.0ms	(.f64 (.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
70.0ms	(+.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)))
50.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 4206 to 3350 computations (20.4% saved)

simplify106.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4909	3818
1	4909	3818

prune527.0ms (0.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	106	5	111

Error

0.2b

Counts

111 → 5

Compiler

Compiled 8793 to 6651 computations (24.4% saved)

regimes700.0ms (1.2%)

Accuracy

Total 0.2b remaining (41.2%)

Threshold costs 0.2b (41.2%)

Compiler

Compiled 10372 to 8654 computations (16.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	117
1	105	117

end0.0ms (0%)

sample47.8s (81.4%)

Algorithm

1×

intervals

Results

41.0s	3718×	body	8192	exit
2.4s	8000×	body	128	valid
203.0ms	11806×	pre	128	true
29.0ms	88×	body	128	invalid

Compiler

Compiled 5263 to 4391 computations (16.6% saved)

Details

analyze1.8s (3.1%)

sample1.1s (1.9%)

simplify49.0ms (0.1%)

prune12.0ms (0%)

localize56.0ms (0.1%)

rewrite1.1s (1.8%)

series213.0ms (0.4%)

simplify76.0ms (0.1%)

prune1.1s (1.9%)

localize55.0ms (0.1%)

rewrite460.0ms (0.8%)

series350.0ms (0.6%)

simplify62.0ms (0.1%)

prune445.0ms (0.8%)

localize55.0ms (0.1%)

rewrite576.0ms (1%)

series395.0ms (0.7%)

simplify87.0ms (0.1%)

prune484.0ms (0.8%)

localize52.0ms (0.1%)

rewrite607.0ms (1%)

series394.0ms (0.7%)

simplify106.0ms (0.2%)

prune527.0ms (0.9%)

regimes700.0ms (1.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample47.8s (81.4%)

Profiling