Details

analyze1.8s (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)

sample1.4s (2.4%)

Algorithm

1×

intervals

Results

1.3s	116×	body	8192	exit
81.0ms	256×	body	128	valid
7.0ms	373×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify136.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune13.0ms (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

Merged error: 1.8b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize60.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.7b	(-.f64 (-.f64 1 z) 1)
4.7b	(-.f64 (-.f64 1 z) 1)
4.7b	(-.f64 (-.f64 1 z) 1)
4.7b	(-.f64 (-.f64 1 z) 1)

rewrite66.0ms (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:

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)

series36.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5392	704

prune1.3s (2.3%)

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

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

rewrite164.0ms (0.3%)

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:

94.0ms	(+.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)))
23.0ms	(+.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))

series158.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

97.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
45.0ms	(+.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)))
15.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify109.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4953	7992
1	4953	7992

prune825.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	90	8	98

Merged error: 0.2b

Counts

98 → 8

Compiler

Compiled 11466 to 9018 computations (21.4% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.3b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 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))

rewrite36.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2487`
15×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
14×	`add-exp-log_binary64_2503`
13×	`add-cbrt-cube_binary64_2501`
11×	`pow1_binary64_2526`
9×	`times-frac_binary64_2471`
8×	`prod-exp_binary64_2514`
7×	`associate-r_binary64_2405`
4×	`add-log-exp_binary64_2504` `associate-l_binary64_2406` `cbrt-unprod_binary64_2498`
3×	`associate-/r_binary64_2409` `pow-prod-down_binary64_2536` `associate-/l_binary64_2410`
2×	`*-commutative_binary64_2396` `sqrt-pow1_binary64_2483`
1×	`associate-l/_binary64_2408` `pow-sub_binary64_2541` `sqrt-prod_binary64_2481` `pow1/2_binary64_2545` `associate-r/_binary64_2407` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `pow-exp_binary64_2533` `unswap-sqr_binary64_2433` `pow-to-exp_binary64_2534` `div-exp_binary64_2516` `div-inv_binary64_2462` `frac-2neg_binary64_2476` `exp-sum_binary64_2511`

Counts

4 → 77

Calls

4 calls:

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)))
4.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
4.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series140.0ms (0.2%)

Counts

4 → 10

Calls

4 calls:

95.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
32.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
12.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify66.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5157	1621

prune273.0ms (0.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 0.0b

Counts

95 → 13

Compiler

Compiled 5503 to 3771 computations (31.5% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.3b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
1.0b	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 z)) (exp.f64 -15/2))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite37.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2487` `add-cbrt-cube_binary64_2501`
15×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503`
14×	`pow1_binary64_2526`
13×	`prod-exp_binary64_2514`
9×	`times-frac_binary64_2471`
7×	`cbrt-unprod_binary64_2498`
6×	`associate-r_binary64_2405`
5×	`pow-prod-down_binary64_2536`
4×	`add-log-exp_binary64_2504` `associate-l_binary64_2406`
3×	`associate-/r_binary64_2409` `associate-/l_binary64_2410`
2×	`associate-l/_binary64_2408` `-commutative_binary64_2396` `sqrt-pow1_binary64_2483`
1×	`pow-sub_binary64_2541` `sqrt-prod_binary64_2481` `pow1/2_binary64_2545` `associate-*r/_binary64_2407` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `pow-exp_binary64_2533` `unswap-sqr_binary64_2433` `pow-to-exp_binary64_2534` `div-exp_binary64_2516` `div-inv_binary64_2462` `frac-2neg_binary64_2476`

Counts

4 → 79

Calls

4 calls:

17.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 z)) (exp.f64 -15/2))
4.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
3.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series176.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

132.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 z)) (exp.f64 -15/2))
31.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
13.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4979	1629
1	4979	1629

prune219.0ms (0.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	89	13	102

Merged error: 0.0b

Counts

102 → 13

Compiler

Compiled 4275 to 2726 computations (36.2% saved)

regimes628.0ms (1.1%)

Compiler: Compiled 8986 to 7248 computations (19.3% saved)

bsearch0.0ms (0%)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	205	589
1	205	589

end0.0ms (0%)

sample49.2s (86.2%)

Algorithm

1×

intervals

Results

42.7s	3883×	body	8192	exit
2.4s	8000×	body	128	valid
232.0ms	11955×	pre	128	true
23.0ms	72×	body	128	invalid

Compiler

Compiled 4885 to 3953 computations (19.1% saved)

Details

analyze1.8s (3.1%)

sample1.4s (2.4%)

simplify136.0ms (0.2%)

prune13.0ms (0%)

localize60.0ms (0.1%)

rewrite66.0ms (0.1%)

series36.0ms (0.1%)

simplify75.0ms (0.1%)

prune1.3s (2.3%)

localize55.0ms (0.1%)

rewrite164.0ms (0.3%)

series158.0ms (0.3%)

simplify109.0ms (0.2%)

prune825.0ms (1.4%)

localize32.0ms (0.1%)

rewrite36.0ms (0.1%)

series140.0ms (0.2%)

simplify66.0ms (0.1%)

prune273.0ms (0.5%)

localize34.0ms (0.1%)

rewrite37.0ms (0.1%)

series176.0ms (0.3%)

simplify78.0ms (0.1%)

prune219.0ms (0.4%)

regimes628.0ms (1.1%)

bsearch0.0ms (0%)

simplify9.0ms (0%)

end0.0ms (0%)

sample49.2s (86.2%)

Profiling