Details

analyze1.7s (2.7%)

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 (2.6%)

Algorithm

1×

intervals

Results

1.5s	125×	body	5120	exit
75.0ms	256×	body	80	valid
7.0ms	384×	pre	80	true
1.0ms	3×	body	80	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify66.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4654	115
1	4654	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)

localize54.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.8b	(-.f64 (-.f64 1 z) 1)
4.8b	(-.f64 (-.f64 1 z) 1)
4.8b	(-.f64 (-.f64 1 z) 1)
4.8b	(-.f64 (-.f64 1 z) 1)

rewrite37.0ms (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` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 76

Calls

4 calls:

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

series7.0ms (0%)

Counts

4 → 12

Calls

4 calls:

2.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(-.f64 (-.f64 1 z) 1)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5349	660

prune678.0ms (1.1%)

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)

localize55.0ms (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 (+.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	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite141.0ms (0.2%)

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`
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 → 86

Calls

4 calls:

96.0ms	(+.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)))
22.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
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)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series38.0ms (0.1%)

Counts

4 → 10

Calls

4 calls:

21.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
12.0ms	(+.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)))
4.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify97.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5038	8025

prune632.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	92	6	98

Merged error: 0.3b

Counts

98 → 6

Compiler

Compiled 11324 to 8902 computations (21.4% saved)

localize96.0ms (0.2%)

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))))

rewrite98.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
12×	`distribute-lft-out_binary64` `sum-log_binary64`
8×	`flip3-+_binary64` `frac-add_binary64` `flip-+_binary64`
4×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `associate-+r+_binary64`

Counts

4 → 68

Calls

4 calls:

26.0ms	(+.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))))
23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series16.0ms (0%)

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
4.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
4.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
4.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5151	2204

prune4.2s (6.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	80	6	86

Merged error: 0.3b

Counts

86 → 6

Compiler

Compiled 32525 to 26865 computations (17.4% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
0.3b	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (.f64 z 58027045549583850709031327/132816557330708771635200) (+.f64 (.f64 (*.f64 z z) 2533639962396748701166118939/4648579506574807007232000) 777369958913643152449373/2951479051793528258560)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 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))

rewrite74.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-exp-log_binary64`
43×	`add-cbrt-cube_binary64` `prod-exp_binary64`
28×	`associate-*r/_binary64`
23×	`cbrt-unprod_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`pow1_binary64` `times-frac_binary64`
17×	`frac-times_binary64`
14×	`associate-l_binary64` `associate-*l/_binary64`
11×	`pow-sub_binary64`
8×	`pow-prod-down_binary64` `flip3-+_binary64` `frac-add_binary64` `flip-+_binary64`
7×	`div-exp_binary64`
5×	`associate-r_binary64` `cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
3×	`pow-to-exp_binary64` `associate-/r_binary64` `associate-/l_binary64` `pow-exp_binary64`
2×	`sqrt-pow1_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `clear-num_binary64` `exp-sum_binary64` `frac-2neg_binary64` `sqrt-prod_binary64`

Counts

4 → 127

Calls

4 calls:

41.0ms	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (.f64 z 58027045549583850709031327/132816557330708771635200) (+.f64 (.f64 (*.f64 z z) 2533639962396748701166118939/4648579506574807007232000) 777369958913643152449373/2951479051793528258560)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 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)))
4.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series71.0ms (0.1%)

Counts

4 → 10

Calls

4 calls:

42.0ms	(.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (.f64 z 58027045549583850709031327/132816557330708771635200) (+.f64 (.f64 (*.f64 z z) 2533639962396748701166118939/4648579506574807007232000) 777369958913643152449373/2951479051793528258560)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
22.0ms	(.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 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify106.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5132	7275

prune300.0ms (0.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	132	11	143

Merged error: 0b

Counts

143 → 11

Compiler

Compiled 7404 to 4931 computations (33.4% saved)

regimes183.0ms (0.3%)

Compiler: Compiled 2650 to 2180 computations (17.7% saved)

bsearch0.0ms (0%)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	206	589
1	206	589

end0.0ms (0%)

sample51.6s (83.2%)

Algorithm

1×

intervals

Results

47.3s	3939×	body	5120	exit
2.4s	8000×	body	80	valid
222.0ms	12046×	pre	80	true
37.0ms	107×	body	80	invalid

Compiler

Compiled 1717 to 1419 computations (17.4% saved)

Details

analyze1.7s (2.7%)

sample1.6s (2.6%)

simplify66.0ms (0.1%)

prune13.0ms (0%)

localize54.0ms (0.1%)

rewrite37.0ms (0.1%)

series7.0ms (0%)

simplify93.0ms (0.1%)

prune678.0ms (1.1%)

localize55.0ms (0.1%)

rewrite141.0ms (0.2%)

series38.0ms (0.1%)

simplify97.0ms (0.2%)

prune632.0ms (1%)

localize96.0ms (0.2%)

rewrite98.0ms (0.2%)

series16.0ms (0%)

simplify93.0ms (0.1%)

prune4.2s (6.7%)

localize34.0ms (0.1%)

rewrite74.0ms (0.1%)

series71.0ms (0.1%)

simplify106.0ms (0.2%)

prune300.0ms (0.5%)

regimes183.0ms (0.3%)

bsearch0.0ms (0%)

simplify10.0ms (0%)

end0.0ms (0%)

sample51.6s (83.2%)

Profiling