Details

analyze2.3s (2.6%)

Algorithm

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)

sample2.2s (2.4%)

Algorithm

1×

intervals

Results

2.0s	144×	body	8192	exit
99.0ms	256×	body	128	valid
8.0ms	405×	pre	128	true
2.0ms	5×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify166.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

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)

localize80.0ms (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))
2.5b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite528.0ms (0.6%)

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:

35.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
34.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
19.0ms	(.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)

series477.0ms (0.5%)

Error

1.1b

Counts

4 → 20

Calls

4 calls:

272.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
61.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
60.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.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 3676 to 2954 computations (19.6% saved)

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5563	2799

prune615.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Error

1.1b

Counts

92 → 7

Compiler

Compiled 8024 to 6194 computations (22.8% saved)

localize90.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 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))
3.1b	(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))

rewrite3.2s (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

183×	`times-frac_binary64_2471`
162×	`*-un-lft-identity_binary64_2465`
156×	`add-sqr-sqrt_binary64_2487`
111×	`cancel-sign-sub-inv_binary64_2431`
76×	`add-cube-cbrt_binary64_2500`
39×	`difference-of-squares_binary64_2434`
36×	`distribute-lft-out--_binary64_2417`
16×	`pow1_binary64_2526`
12×	`add-exp-log_binary64_2503` `flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-/r/_binary64_2411`
11×	`add-cbrt-cube_binary64_2501`
8×	`frac-times_binary64_2475` `frac-sub_binary64_2474` `prod-exp_binary64_2514` `associate-r_binary64_2405`
7×	`flip3--_binary64_2469` `flip--_binary64_2440`
6×	`add-log-exp_binary64_2504` `div-inv_binary64_2462` `swap-sqr_binary64_2432` `distribute-lft-out_binary64_2416`
5×	`associate-l/_binary64_2408` `associate-r/_binary64_2407` `associate-l_binary64_2406`
4×	`cbrt-unprod_binary64_2498`
3×	`pow-prod-down_binary64_2536`
2×	`distribute-rgt-in_binary64_2415` `associate--l+_binary64_2402` `distribute-lft-in_binary64_2414` `sqrt-pow1_binary64_2483` `*-commutative_binary64_2396`
1×	`diff-log_binary64_2557` `sub-neg_binary64_2458` `pow1/2_binary64_2545` `sqrt-prod_binary64_2481` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `pow-sub_binary64_2541` `exp-sum_binary64_2511` `pow2_binary64_2546` `pow-prod-up_binary64_2535` `pow-plus_binary64_2528` `pow-sqr_binary64_2438` `unswap-sqr_binary64_2433`

Counts

4 → 207

Calls

4 calls:

105.0ms	(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
26.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
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)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 24141 to 19104 computations (20.9% saved)

series501.0ms (0.6%)

Error

1.1b

Counts

4 → 24

Calls

4 calls:

221.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
76.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
52.0ms	(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 5408 to 4386 computations (18.9% saved)

simplify166.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4931	7517
1	4931	7517

prune3.2s (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	6	0	6
Picked	0	1	1
Done	0	0	0
Total	234	4	238

Error

0.3b

Counts

238 → 4

Compiler

Compiled 25742 to 20217 computations (21.5% saved)

localize67.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 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)
3.1b	(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))

rewrite3.3s (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

183×	`times-frac_binary64_2471`
163×	`*-un-lft-identity_binary64_2465`
158×	`add-sqr-sqrt_binary64_2487`
111×	`cancel-sign-sub-inv_binary64_2431`
77×	`add-cube-cbrt_binary64_2500`
39×	`difference-of-squares_binary64_2434`
36×	`distribute-lft-out--_binary64_2417`
20×	`add-exp-log_binary64_2503`
17×	`prod-exp_binary64_2514`
15×	`add-cbrt-cube_binary64_2501`
14×	`pow1_binary64_2526`
12×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-/r/_binary64_2411`
8×	`frac-times_binary64_2475` `frac-sub_binary64_2474` `associate-r_binary64_2405`
7×	`flip3--_binary64_2469` `flip--_binary64_2440` `cbrt-unprod_binary64_2498`
6×	`add-log-exp_binary64_2504` `div-inv_binary64_2462` `swap-sqr_binary64_2432` `distribute-lft-out_binary64_2416`
5×	`associate-l/_binary64_2408` `associate-r/_binary64_2407` `associate-l_binary64_2406`
3×	`sqrt-prod_binary64_2481`
2×	`distribute-rgt-in_binary64_2415` `associate--l+_binary64_2402` `distribute-lft-in_binary64_2414` `pow-prod-down_binary64_2536` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `*-commutative_binary64_2396`
1×	`diff-log_binary64_2557` `sub-neg_binary64_2458` `pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `pow-sub_binary64_2541` `exp-sum_binary64_2511` `pow2_binary64_2546` `pow-prod-up_binary64_2535` `pow-plus_binary64_2528` `pow-sqr_binary64_2438` `unswap-sqr_binary64_2433`

Counts

4 → 213

Calls

4 calls:

76.0ms	(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
34.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
26.0ms	(.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 25014 to 19595 computations (21.7% saved)

series524.0ms (0.6%)

Error

0.3b

Counts

4 → 24

Calls

4 calls:

242.0ms	(.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)))
80.0ms	(*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
55.0ms	(-.f64 (*.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (/.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (-.f64 2 z)) (-.f64 2 z)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 5446 to 4406 computations (19.1% saved)

simplify149.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4954	7682
1	4954	7682

prune3.4s (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	236	5	241

Error

0.3b

Counts

241 → 5

Compiler

Compiled 26601 to 20701 computations (22.2% saved)

localize95.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)
1.0b	(cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
3.1b	(+.f64 (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)) (-.f64 2 z))) (/.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (-.f64 2 z))))

rewrite845.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

24×	`frac-add_binary64_2473`
20×	`frac-times_binary64_2475`
19×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
16×	`distribute-neg-frac_binary64_2429`
14×	`associate-l/_binary64_2408` `associate-r/_binary64_2407`
7×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465` `cbrt-prod_binary64_2496`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
2×	`associate-+l+_binary64_2398` `sqrt-pow1_binary64_2483` `pow1/3_binary64_2547`
1×	`sum-log_binary64_2556` `distribute-lft-neg-out_binary64_2424` `unsub-neg_binary64_2459` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `+-commutative_binary64_2395` `pow1/2_binary64_2545` `pow-prod-down_binary64_2536` `sqrt-prod_binary64_2481`

Counts

4 → 71

Calls

4 calls:

31.0ms	(+.f64 (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)) (-.f64 2 z))) (/.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (-.f64 2 z))))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))
1.0ms	(cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)
1.0ms	(cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)

Compiler

Compiled 9679 to 7881 computations (18.6% saved)

series131.0ms (0.1%)

Error

0.3b

Counts

4 → 6

Calls

4 calls:

107.0ms	(+.f64 (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)) (-.f64 2 z))) (/.f64 (cbrt.f64 30666706506962181608371823434969/19342813113834066795298816) (-.f64 2 z))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)
0.0ms	(cbrt.f64 30666706506962181608371823434969/19342813113834066795298816)

Compiler

Compiled 1312 to 1079 computations (17.8% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4987	3328
1	4987	3328

prune788.0ms (0.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	77	5	82

Error

0.3b

Counts

82 → 5

Compiler

Compiled 9256 to 7394 computations (20.1% saved)

regimes1.1s (1.2%)

Accuracy

Total 0.2b remaining (38.1%)

Threshold costs 0.2b (38.1%)

Compiler

Compiled 13626 to 11394 computations (16.4% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	147	156
1	147	156

end0.0ms (0%)

sample1.1min (73%)

Algorithm

1×

intervals

Results

54.9s	4016×	body	8192	exit
3.0s	8000×	body	128	valid
256.0ms	12113×	pre	128	true
47.0ms	97×	body	128	invalid

Compiler

Compiled 6916 to 5783 computations (16.4% saved)

Details

analyze2.3s (2.6%)

sample2.2s (2.4%)

simplify166.0ms (0.2%)

prune12.0ms (0%)

localize80.0ms (0.1%)

rewrite528.0ms (0.6%)

series477.0ms (0.5%)

simplify82.0ms (0.1%)

prune615.0ms (0.7%)

localize90.0ms (0.1%)

rewrite3.2s (3.6%)

series501.0ms (0.6%)

simplify166.0ms (0.2%)

prune3.2s (3.6%)

localize67.0ms (0.1%)

rewrite3.3s (3.7%)

series524.0ms (0.6%)

simplify149.0ms (0.2%)

prune3.4s (3.8%)

localize95.0ms (0.1%)

rewrite845.0ms (0.9%)

series131.0ms (0.1%)

simplify98.0ms (0.1%)

prune788.0ms (0.9%)

regimes1.1s (1.2%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample1.1min (73%)

Profiling