Details

analyze1.7s (3.1%)

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)

sample1.6s (2.9%)

Algorithm

1×

intervals

Results

1.5s	135×	body	8192	exit
72.0ms	256×	body	128	valid
7.0ms	391×	pre	128	true

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify140.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune16.0ms (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)

localize55.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.3b	(-.f64 (-.f64 1 z) 1)
4.3b	(-.f64 (-.f64 1 z) 1)
4.3b	(-.f64 (-.f64 1 z) 1)
4.3b	(-.f64 (-.f64 1 z) 1)

rewrite59.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

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×	`add-cube-cbrt_binary64_2500` `distribute-lft-out--_binary64_2417` `diff-log_binary64_2557`
8×	`difference-of-squares_binary64_2434` `sub-neg_binary64_2458`
4×	`difference-of-sqr-1_binary64_2435` `flip--_binary64_2440` `associate--l-_binary64_2403` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526` `flip3--_binary64_2469`

Counts

4 → 100

Calls

4 calls:

9.0ms	(-.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)

series156.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(-.f64 (-.f64 1 z) 1)
39.0ms	(-.f64 (-.f64 1 z) 1)
38.0ms	(-.f64 (-.f64 1 z) 1)
37.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 2904 to 2592 computations (10.7% saved)

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5392	704

prune1.0s (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)

localize52.0ms (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)))

rewrite90.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_2465`
18×	`add-log-exp_binary64_2504`
10×	`add-exp-log_binary64_2503`
9×	`sum-log_binary64_2556` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526` `distribute-lft-out_binary64_2416`
8×	`frac-add_binary64_2473`
7×	`prod-exp_binary64_2514`
5×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
4×	`associate-r_binary64_2405`
3×	`cbrt-unprod_binary64_2498`
2×	`+-commutative_binary64_2395` `associate-+l+_binary64_2398` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483`
1×	`associate-l/_binary64_2408` `pow-sub_binary64_2541` `-commutative_binary64_2396` `sqrt-prod_binary64_2481` `pow1/2_binary64_2545` `associate-r/_binary64_2407` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `exp-sum_binary64_2511` `associate-l*_binary64_2406`

Counts

4 → 70

Calls

4 calls:

33.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
24.0ms	(+.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))

series268.0ms (0.5%)

Counts

4 → 20

Calls

4 calls:

179.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
47.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
41.0ms	(+.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 2052 to 1704 computations (17% saved)

simplify67.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5563	2799

prune505.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	84	8	92

Error

1.1b

Counts

92 → 8

Compiler

Compiled 8025 to 6196 computations (22.8% saved)

localize58.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (+.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))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 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))

rewrite199.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_2465`
48×	`add-log-exp_binary64_2504`
34×	`sum-log_binary64_2556` `distribute-lft-out_binary64_2416`
32×	`frac-add_binary64_2473`
10×	`add-exp-log_binary64_2503`
9×	`add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
8×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
7×	`prod-exp_binary64_2514`
5×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
4×	`associate-r_binary64_2405`
3×	`cbrt-unprod_binary64_2498`
2×	`+-commutative_binary64_2395` `associate-+l+_binary64_2398` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483`
1×	`associate-l/_binary64_2408` `pow-sub_binary64_2541` `-commutative_binary64_2396` `sqrt-prod_binary64_2481` `pow1/2_binary64_2545` `associate-r/_binary64_2407` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `exp-sum_binary64_2511` `associate-l*_binary64_2406`

Counts

4 → 86

Calls

4 calls:

107.0ms	(+.f64 (+.f64 (+.f64 (+.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))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 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)))
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))

series309.0ms (0.6%)

Counts

4 → 22

Calls

4 calls:

194.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
63.0ms	(+.f64 (+.f64 (+.f64 (+.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))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
51.0ms	(+.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 1904 to 1580 computations (17% saved)

simplify110.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4977	7898
1	4977	7898

prune725.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	108	8	116

Error

0.2b

Counts

116 → 8

Compiler

Compiled 11307 to 8838 computations (21.8% saved)

localize54.0ms (0.1%)

Local error

Found 4 expressions with local error:

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 -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))

rewrite115.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_2465`
15×	`add-log-exp_binary64_2504`
11×	`distribute-lft-out_binary64_2416`
10×	`add-exp-log_binary64_2503`
9×	`add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
8×	`times-frac_binary64_2471`
7×	`sum-log_binary64_2556` `prod-exp_binary64_2514`
5×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
4×	`distribute-lft-out--_binary64_2417` `associate-r_binary64_2405`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `frac-add_binary64_2473` `cbrt-unprod_binary64_2498`
2×	`+-commutative_binary64_2395` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483`
1×	`associate-l/_binary64_2408` `pow-sub_binary64_2541` `-commutative_binary64_2396` `sqrt-prod_binary64_2481` `pow1/2_binary64_2545` `associate-+l+_binary64_2398` `associate-r/_binary64_2407` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `exp-sum_binary64_2511` `associate-l*_binary64_2406`

Counts

4 → 68

Calls

4 calls:

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)))
34.0ms	(+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 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))

series309.0ms (0.6%)

Counts

4 → 22

Calls

4 calls:

197.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
57.0ms	(+.f64 (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 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)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 2255 to 1875 computations (16.9% saved)

simplify63.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5124	2508

prune448.0ms (0.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	90	8	98

Error

0.2b

Counts

98 → 8

Compiler

Compiled 7270 to 5569 computations (23.4% saved)

regimes406.0ms (0.7%)

Accuracy

Total 0.2b remaining (40%)

Threshold costs 0.2b (40%)

Compiler

Compiled 5866 to 4900 computations (16.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	104	115
1	104	115

end0.0ms (0%)

sample45.9s (84.3%)

Algorithm

1×

intervals

Results

41.0s	3754×	body	8192	exit
2.3s	8000×	body	128	valid
214.0ms	11846×	pre	128	true
29.0ms	92×	body	128	invalid

Compiler

Compiled 3009 to 2513 computations (16.5% saved)

Details

analyze1.7s (3.1%)

sample1.6s (2.9%)

simplify140.0ms (0.3%)

prune16.0ms (0%)

localize55.0ms (0.1%)

rewrite59.0ms (0.1%)

series156.0ms (0.3%)

simplify75.0ms (0.1%)

prune1.0s (1.9%)

localize52.0ms (0.1%)

rewrite90.0ms (0.2%)

series268.0ms (0.5%)

simplify67.0ms (0.1%)

prune505.0ms (0.9%)

localize58.0ms (0.1%)

rewrite199.0ms (0.4%)

series309.0ms (0.6%)

simplify110.0ms (0.2%)

prune725.0ms (1.3%)

localize54.0ms (0.1%)

rewrite115.0ms (0.2%)

series309.0ms (0.6%)

simplify63.0ms (0.1%)

prune448.0ms (0.8%)

regimes406.0ms (0.7%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample45.9s (84.3%)

Profiling