Details

analyze1.8s (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)

sample1.6s (2.8%)

Algorithm

1×

intervals

Results

1.5s	126×	body	5120	exit
84.0ms	256×	body	80	valid
8.0ms	383×	pre	80	true
0.0ms	1×	body	80	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify99.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4777	115
1	4777	115

prune15.0ms (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: 1.7b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize60.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(-.f64 (-.f64 1 z) 1)
6.1b	(-.f64 (-.f64 1 z) 1)
6.1b	(-.f64 (-.f64 1 z) 1)
6.1b	(-.f64 (-.f64 1 z) 1)

rewrite42.0ms (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)

series79.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(-.f64 (-.f64 1 z) 1)
20.0ms	(-.f64 (-.f64 1 z) 1)
18.0ms	(-.f64 (-.f64 1 z) 1)
18.0ms	(-.f64 (-.f64 1 z) 1)

simplify131.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4905	680
1	4905	680

prune932.0ms (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: 1.7b

Counts

94 → 2

Compiler

Compiled 11534 to 9706 computations (15.8% 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))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite157.0ms (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:

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)))
25.0ms	(+.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))

series320.0ms (0.5%)

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)))
95.0ms	(+.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))

simplify161.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4942	8117
1	4942	8117

prune863.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	92	8	100
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	94	8	102

Merged error: 0.2b

Counts

102 → 8

Compiler

Compiled 11393 to 8937 computations (21.6% saved)

localize35.0ms (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))

rewrite36.0ms (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))

series285.0ms (0.5%)

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)))
54.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
39.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify110.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4981	1733
1	4981	1733

prune259.0ms (0.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	90	10	100

Merged error: 0.0b

Counts

100 → 10

Compiler

Compiled 4926 to 3263 computations (33.8% saved)

localize49.0ms (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)

rewrite33.0ms (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:

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)))
6.0ms	(*.f64 (pow.f64 PI.f64 4) 7/360)
3.0ms	(pow.f64 PI.f64 4)
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series190.0ms (0.3%)

Counts

4 → 6

Calls

4 calls:

190.0ms	(.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	(*.f64 (pow.f64 PI.f64 4) 7/360)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify140.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4939	1587
1	4939	1587

prune274.0ms (0.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	84	10	94

Merged error: 0.0b

Counts

94 → 10

Compiler

Compiled 5181 to 3956 computations (23.6% saved)

regimes61.0ms (0.1%)

Compiler: Compiled 596 to 449 computations (24.7% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	78	89
1	78	89

end0.0ms (0%)

sample50.8s (86.7%)

Algorithm

1×

intervals

Results

47.0s	3948×	body	5120	exit
2.5s	8000×	body	80	valid
241.0ms	12044×	pre	80	true
32.0ms	96×	body	80	invalid

Compiler

Compiled 777 to 606 computations (22% saved)

Details

analyze1.8s (3%)

sample1.6s (2.8%)

simplify99.0ms (0.2%)

prune15.0ms (0%)

localize60.0ms (0.1%)

rewrite42.0ms (0.1%)

series79.0ms (0.1%)

simplify131.0ms (0.2%)

prune932.0ms (1.6%)

localize55.0ms (0.1%)

rewrite157.0ms (0.3%)

series320.0ms (0.5%)

simplify161.0ms (0.3%)

prune863.0ms (1.5%)

localize35.0ms (0.1%)

rewrite36.0ms (0.1%)

series285.0ms (0.5%)

simplify110.0ms (0.2%)

prune259.0ms (0.4%)

localize49.0ms (0.1%)

rewrite33.0ms (0.1%)

series190.0ms (0.3%)

simplify140.0ms (0.2%)

prune274.0ms (0.5%)

regimes61.0ms (0.1%)

bsearch0.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample50.8s (86.7%)

Profiling