Details

analyze1.7s (1.9%)

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)

sample1.4s (1.5%)

Algorithm

1×

intervals

Results

1.2s	111×	body	8192	exit
84.0ms	256×	body	128	valid
11.0ms	372×	pre	128	true
2.0ms	5×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify143.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune17.0ms (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)

localize52.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (+.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))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.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))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite174.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_2465`
44×	`add-log-exp_binary64_2504` `frac-add_binary64_2473`
31×	`sum-log_binary64_2556` `distribute-lft-out_binary64_2416`
10×	`add-exp-log_binary64_2503`
9×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
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:

105.0ms	(+.f64 (+.f64 (+.f64 (+.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))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
26.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.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)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series325.0ms (0.4%)

Counts

4 → 22

Calls

4 calls:

198.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
83.0ms	(+.f64 (+.f64 (+.f64 (+.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))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
43.0ms	(+.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 1946 to 1620 computations (16.8% saved)

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5269	8324

prune835.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	8	110

Error

0.3b

Counts

110 → 8

Compiler

Compiled 12370 to 9719 computations (21.4% saved)

localize93.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite162.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_2465` `add-log-exp_binary64_2504`
12×	`sum-log_binary64_2556` `distribute-lft-out_binary64_2416`
8×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `frac-add_binary64_2473`
4×	`+-commutative_binary64_2395` `add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-sqr-sqrt_binary64_2487` `add-cbrt-cube_binary64_2501` `associate-+r+_binary64_2397` `pow1_binary64_2526`

Counts

4 → 68

Calls

4 calls:

31.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
29.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
26.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
26.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series796.0ms (0.9%)

Counts

4 → 47

Calls

4 calls:

202.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
199.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
198.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
196.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

Compiler

Compiled 18600 to 15600 computations (16.1% saved)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5026	2557

prune6.1s (6.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	116	7	123

Error

0.3b

Counts

123 → 7

Compiler

Compiled 46605 to 38480 computations (17.4% saved)

localize108.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite159.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_2465` `add-log-exp_binary64_2504`
12×	`sum-log_binary64_2556` `distribute-lft-out_binary64_2416`
8×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `frac-add_binary64_2473`
4×	`+-commutative_binary64_2395` `add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-sqr-sqrt_binary64_2487` `add-cbrt-cube_binary64_2501` `associate-+r+_binary64_2397` `pow1_binary64_2526`

Counts

4 → 68

Calls

4 calls:

27.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
24.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series875.0ms (1%)

Counts

4 → 48

Calls

4 calls:

220.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
219.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
219.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
217.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

Compiler

Compiled 20088 to 16896 computations (15.9% saved)

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5026	2576

prune7.0s (7.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	116	7	123

Error

0.3b

Counts

123 → 7

Compiler

Compiled 50170 to 41579 computations (17.1% saved)

localize86.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 -5537752839100187/4398046511104 (-.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))
2.8b	(+.f64 (.f64 (-.f64 2 z) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z)))) (.f64 -5537752839100187/4398046511104 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))

rewrite457.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

577×	`times-frac_binary64_2471`
512×	`add-sqr-sqrt_binary64_2487`
507×	`*-un-lft-identity_binary64_2465`
396×	`cancel-sign-sub-inv_binary64_2431`
302×	`associate-+l+_binary64_2398`
217×	`add-cube-cbrt_binary64_2500`
201×	`distribute-lft-in_binary64_2414` `distribute-rgt-in_binary64_2415`
194×	`difference-of-squares_binary64_2434`
97×	`distribute-lft-out--_binary64_2417`
50×	`associate-+r+_binary64_2397`
39×	`flip--_binary64_2440` `flip3--_binary64_2469`
36×	`associate-/r/_binary64_2411`
23×	`associate-*r/_binary64_2407`
18×	`div-inv_binary64_2462`
16×	`frac-add_binary64_2473`
12×	`add-exp-log_binary64_2503`
11×	`add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
10×	`associate-r_binary64_2405`
8×	`frac-times_binary64_2475` `prod-exp_binary64_2514`
6×	`add-log-exp_binary64_2504` `sub-neg_binary64_2458`
5×	`associate-*l/_binary64_2408`
4×	`associate-l_binary64_2406` `cbrt-unprod_binary64_2498`
3×	`pow-prod-down_binary64_2536`
2×	`*-commutative_binary64_2396` `sqrt-pow1_binary64_2483`
1×	`flip3-+_binary64_2468` `pow-sub_binary64_2541` `sqrt-prod_binary64_2481` `+-commutative_binary64_2395` `sum-log_binary64_2556` `pow1/2_binary64_2545` `flip-+_binary64_2439` `pow-exp_binary64_2533` `unswap-sqr_binary64_2433` `pow-to-exp_binary64_2534` `exp-sum_binary64_2511`

Counts

4 → 484

Calls

4 calls:

119.0ms	(+.f64 (.f64 (-.f64 2 z) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z)))) (.f64 -5537752839100187/4398046511104 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))
20.0ms	(*.f64 -5537752839100187/4398046511104 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 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))

series391.0ms (0.4%)

Counts

4 → 18

Calls

4 calls:

224.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
93.0ms	(+.f64 (.f64 (-.f64 2 z) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (-.f64 1 z)) (-.f64 1 z)))) (.f64 -5537752839100187/4398046511104 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))
74.0ms	(*.f64 -5537752839100187/4398046511104 (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 5385 to 4363 computations (19% saved)

simplify266.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

502 → 502

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5011	23573

prune21.1s (23.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	499	3	502
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	502	7	509

Error

0.3b

Counts

509 → 7

Compiler

Compiled 117141 to 91919 computations (21.5% saved)

regimes655.0ms (0.7%)

Accuracy

Total 0.2b remaining (41.1%)

Threshold costs 0.2b (41.1%)

Compiler

Compiled 10246 to 8434 computations (17.7% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	232	460
1	232	460

end0.0ms (0%)

sample48.0s (52.6%)

Algorithm

1×

intervals

Results

41.6s	3780×	body	8192	exit
2.4s	8000×	body	128	valid
227.0ms	11893×	pre	128	true
39.0ms	113×	body	128	invalid

Compiler

Compiled 5429 to 4467 computations (17.7% saved)

Details

analyze1.7s (1.9%)

sample1.4s (1.5%)

simplify143.0ms (0.2%)

prune17.0ms (0%)

localize52.0ms (0.1%)

rewrite174.0ms (0.2%)

series325.0ms (0.4%)

simplify96.0ms (0.1%)

prune835.0ms (0.9%)

localize93.0ms (0.1%)

rewrite162.0ms (0.2%)

series796.0ms (0.9%)

simplify93.0ms (0.1%)

prune6.1s (6.7%)

localize108.0ms (0.1%)

rewrite159.0ms (0.2%)

series875.0ms (1%)

simplify85.0ms (0.1%)

prune7.0s (7.7%)

localize86.0ms (0.1%)

rewrite457.0ms (0.5%)

series391.0ms (0.4%)

simplify266.0ms (0.3%)

prune21.1s (23.1%)

regimes655.0ms (0.7%)

bsearch0.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample48.0s (52.6%)

Profiling