Details

analyze1.7s (3%)

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)

sample1.3s (2.3%)

Algorithm

1×

intervals

Results

1.2s	101×	body	5120	exit
79.0ms	256×	body	80	valid
7.0ms	360×	pre	80	true
1.0ms	3×	body	80	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify102.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4805	115
1	4805	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)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.5b	(-.f64 (-.f64 1 z) 1)
7.5b	(-.f64 (-.f64 1 z) 1)
7.5b	(-.f64 (-.f64 1 z) 1)
7.5b	(-.f64 (-.f64 1 z) 1)

rewrite43.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
24×	`add-log-exp_binary64`
20×	`add-sqr-sqrt_binary64`
12×	`diff-log_binary64` `distribute-lft-out--_binary64`
8×	`sub-neg_binary64` `difference-of-squares_binary64`
4×	`pow1_binary64` `flip3--_binary64` `associate--l-_binary64` `add-cube-cbrt_binary64` `difference-of-sqr-1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 80

Calls

4 calls:

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

series90.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(-.f64 (-.f64 1 z) 1)
23.0ms	(-.f64 (-.f64 1 z) 1)
23.0ms	(-.f64 (-.f64 1 z) 1)
21.0ms	(-.f64 (-.f64 1 z) 1)

simplify166.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4814	680
1	4814	680

prune931.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	92	2	94

Merged error: 1.8b

Counts

94 → 2

Compiler

Compiled 11534 to 9706 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)))

rewrite161.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
44×	`add-log-exp_binary64` `frac-add_binary64`
31×	`distribute-lft-out_binary64` `sum-log_binary64`
10×	`add-exp-log_binary64`
9×	`flip3-+_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
7×	`prod-exp_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`associate-r_binary64` `insert-posit16`
3×	`cbrt-unprod_binary64`
2×	`pow-prod-down_binary64` `associate-+l+_binary64` `sqrt-pow1_binary64` `+-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `associate-r/_binary64` `associate-l_binary64` `pow-sub_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

108.0ms	(+.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)))
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)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series333.0ms (0.6%)

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)))
100.0ms	(+.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)))
33.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify162.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4944	8117
1	4944	8117

prune884.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	92	8	100
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	93	9	102

Merged error: 0.2b

Counts

102 → 9

Compiler

Compiled 11531 to 9053 computations (21.5% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
0.4b	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
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))

rewrite37.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
10×	`prod-exp_binary64`
9×	`times-frac_binary64`
7×	`associate-r_binary64`
6×	`cbrt-unprod_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`associate-l_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `pow-sub_binary64` `exp-sum_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `associate-l/_binary64`

Counts

4 → 82

Calls

4 calls:

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)))
7.0ms	(.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))

series302.0ms (0.5%)

Counts

4 → 10

Calls

4 calls:

199.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
56.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
47.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify111.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5064	1733

prune259.0ms (0.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	80	12	92
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	86	15	101

Merged error: 0.0b

Counts

101 → 15

Compiler

Compiled 5129 to 3403 computations (33.7% saved)

localize46.0ms (0.1%)

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)

rewrite34.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
15×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
8×	`associate-l_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`pow-prod-down_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `associate-r/_binary64` `pow-pow_binary64` `pow-sub_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `associate-l/_binary64`

Counts

4 → 78

Calls

4 calls:

20.0ms	(.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)
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))
3.0ms	(pow.f64 PI.f64 4)

series205.0ms (0.4%)

Counts

4 → 6

Calls

4 calls:

205.0ms	(.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)

simplify142.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune307.0ms (0.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	86	13	99

Merged error: 0.0b

Counts

99 → 13

Compiler

Compiled 5181 to 3956 computations (23.6% saved)

regimes166.0ms (0.3%)

Compiler: Compiled 1860 to 1466 computations (21.2% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	79	91
1	79	91

end0.0ms (0%)

sample49.1s (86.5%)

Algorithm

1×

intervals

Results

45.4s	3817×	body	5120	exit
2.4s	8000×	body	80	valid
223.0ms	11901×	pre	80	true
27.0ms	84×	body	80	invalid

Compiler

Compiled 990 to 782 computations (21% saved)

Details

analyze1.7s (3%)

sample1.3s (2.3%)

simplify102.0ms (0.2%)

prune13.0ms (0%)

localize57.0ms (0.1%)

rewrite43.0ms (0.1%)

series90.0ms (0.2%)

simplify166.0ms (0.3%)

prune931.0ms (1.6%)

localize54.0ms (0.1%)

rewrite161.0ms (0.3%)

series333.0ms (0.6%)

simplify162.0ms (0.3%)

prune884.0ms (1.6%)

localize31.0ms (0.1%)

rewrite37.0ms (0.1%)

series302.0ms (0.5%)

simplify111.0ms (0.2%)

prune259.0ms (0.5%)

localize46.0ms (0.1%)

rewrite34.0ms (0.1%)

series205.0ms (0.4%)

simplify142.0ms (0.3%)

prune307.0ms (0.5%)

regimes166.0ms (0.3%)

bsearch0.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample49.1s (86.5%)

Profiling