Details

analyze1.7s (1.8%)

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)

sample2.4s (2.6%)

Algorithm

1×

intervals

Results

2.3s	107×	body	8192	exit
81.0ms	256×	body	128	valid
10.0ms	368×	pre	128	true
2.0ms	5×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify206.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4776	115
1	4776	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

Merged error: 1.8b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)

rewrite55.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_2436`
24×	`add-log-exp_binary64_2472`
20×	`add-sqr-sqrt_binary64_2457`
12×	`distribute-lft-out--_binary64_2390` `diff-log_binary64_2525`
8×	`sub-neg_binary64_2429` `difference-of-squares_binary64_2405`
4×	`flip3--_binary64_2440` `add-exp-log_binary64_2471` `add-cube-cbrt_binary64_2468` `add-cbrt-cube_binary64_2469` `associate--l-_binary64_2376` `pow1_binary64_2494` `difference-of-sqr-1_binary64_2406` `flip--_binary64_2411` `associate--l+_binary64_2375`

Counts

4 → 76

Calls

4 calls:

9.0ms	(-.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)

series74.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(-.f64 (-.f64 1 z) 1)
18.0ms	(-.f64 (-.f64 1 z) 1)
18.0ms	(-.f64 (-.f64 1 z) 1)
17.0ms	(-.f64 (-.f64 1 z) 1)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4902	660
1	4902	660

prune882.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	88	2	90

Merged error: 1.8b

Counts

90 → 2

Compiler

Compiled 11046 to 9300 computations (15.8% saved)

localize54.0ms (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)))

rewrite176.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_2436`
44×	`frac-add_binary64_2444` `add-log-exp_binary64_2472`
31×	`distribute-lft-out_binary64_2389` `sum-log_binary64_2524`
10×	`add-exp-log_binary64_2471`
9×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494`
7×	`prod-exp_binary64_2482`
5×	`add-sqr-sqrt_binary64_2457` `add-cube-cbrt_binary64_2468`
4×	`associate-r_binary64_2378`
3×	`cbrt-unprod_binary64_2466`
2×	`pow-prod-down_binary64_2504` `associate-+l+_binary64_2371` `+-commutative_binary64_2368` `sqrt-pow1_binary64_2453`
1×	`-commutative_binary64_2369` `pow1/2_binary64_2513` `associate-r/_binary64_2380` `pow-to-exp_binary64_2502` `pow-exp_binary64_2501` `pow-sub_binary64_2509` `sqrt-prod_binary64_2451` `associate-l/_binary64_2381` `associate-l*_binary64_2379` `exp-sum_binary64_2479`

Counts

4 → 86

Calls

4 calls:

102.0ms	(+.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)))
24.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
23.0ms	(.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))

series318.0ms (0.3%)

Counts

4 → 10

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)))
92.0ms	(+.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)))
28.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify112.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4971	7992
1	4971	7992

prune725.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	91	7	98

Merged error: 0.2b

Counts

98 → 7

Compiler

Compiled 11013 to 8642 computations (21.5% saved)

localize31.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
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))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64_2471`
16×	`add-cbrt-cube_binary64_2469`
15×	`add-sqr-sqrt_binary64_2457`
14×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436` `pow1_binary64_2494`
10×	`prod-exp_binary64_2482`
9×	`times-frac_binary64_2442`
7×	`associate-r_binary64_2378`
6×	`cbrt-unprod_binary64_2466`
5×	`pow-prod-down_binary64_2504`
4×	`add-log-exp_binary64_2472`
3×	`associate-/l_binary64_2383` `associate-/r_binary64_2382`
2×	`-commutative_binary64_2369` `associate-l*_binary64_2379` `sqrt-pow1_binary64_2453`
1×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `pow1/2_binary64_2513` `div-exp_binary64_2484` `associate-r/_binary64_2380` `unswap-sqr_binary64_2404` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-exp_binary64_2501` `pow-sub_binary64_2509` `frac-2neg_binary64_2447` `sqrt-prod_binary64_2451` `associate-l/_binary64_2381` `exp-sum_binary64_2479`

Counts

4 → 78

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)))
6.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
4.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series287.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

192.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
60.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
35.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify64.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4975	1673
1	4975	1673

prune230.0ms (0.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 0.0b

Counts

95 → 10

Compiler

Compiled 4733 to 3140 computations (33.7% saved)

localize42.0ms (0%)

Local error

Found 4 expressions with local error:

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	(*.f64 (pow.f64 PI.f64 4) 7/360)
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
1.6b	(pow.f64 PI.f64 4)

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64_2471`
15×	`add-sqr-sqrt_binary64_2457`
11×	`add-cbrt-cube_binary64_2469`
10×	`prod-exp_binary64_2482` `add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436` `pow1_binary64_2494`
8×	`associate-l_binary64_2379`
7×	`unpow-prod-down_binary64_2512` `associate-r_binary64_2378`
4×	`add-log-exp_binary64_2472` `cbrt-unprod_binary64_2466`
3×	`pow-unpow_binary64_2510` `unswap-sqr_binary64_2404` `pow-to-exp_binary64_2502` `pow-exp_binary64_2501` `sqr-pow_binary64_2408`
2×	`*-commutative_binary64_2369` `pow-prod-down_binary64_2504` `sqrt-pow1_binary64_2453`
1×	`pow1/2_binary64_2513` `associate-r/_binary64_2380` `pow-sub_binary64_2509` `pow-pow_binary64_2505` `sqrt-prod_binary64_2451` `associate-l/_binary64_2381` `exp-sum_binary64_2479`

Counts

4 → 74

Calls

4 calls:

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)))
6.0ms	(*.f64 (pow.f64 PI.f64 4) 7/360)
4.0ms	(sqrt.f64 (*.f64 PI.f64 2))
2.0ms	(pow.f64 PI.f64 4)

series209.0ms (0.2%)

Counts

4 → 6

Calls

4 calls:

208.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(*.f64 (pow.f64 PI.f64 4) 7/360)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4933	1532
1	4933	1532

prune280.0ms (0.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 0.0b

Counts

90 → 10

Compiler

Compiled 4945 to 3776 computations (23.6% saved)

regimes59.0ms (0.1%)

Compiler: Compiled 580 to 443 computations (23.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	91
1	78	91

end0.0ms (0%)

sample1.4min (91.1%)

Algorithm

1×

intervals

Results

1.3min	3873×	body	8192	exit
2.5s	8000×	body	128	valid
230.0ms	11974×	pre	128	true
40.0ms	101×	body	128	invalid

Compiler

Compiled 762 to 601 computations (21.1% saved)

Details

analyze1.7s (1.8%)

sample2.4s (2.6%)

simplify206.0ms (0.2%)

prune17.0ms (0%)

localize57.0ms (0.1%)

rewrite55.0ms (0.1%)

series74.0ms (0.1%)

simplify77.0ms (0.1%)

prune882.0ms (1%)

localize54.0ms (0.1%)

rewrite176.0ms (0.2%)

series318.0ms (0.3%)

simplify112.0ms (0.1%)

prune725.0ms (0.8%)

localize31.0ms (0%)

rewrite40.0ms (0%)

series287.0ms (0.3%)

simplify64.0ms (0.1%)

prune230.0ms (0.2%)

localize42.0ms (0%)

rewrite40.0ms (0%)

series209.0ms (0.2%)

simplify72.0ms (0.1%)

prune280.0ms (0.3%)

regimes59.0ms (0.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4min (91.1%)

Profiling