Details

analyze125.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 71 to 33 computations (53.5% saved)

sample45.0ms (0.6%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify114.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1509×	`associate-/l*_binary64`
766×	`distribute-rgt-out_binary64`
744×	`distribute-lft-out_binary64`
549×	`unswap-sqr_binary64`
497×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	32	75
1	74	59
2	239	41
3	928	37
4	1549	37
5	3195	37
6	3534	37
7	3698	33
8	2289	33
9	2775	33
10	2823	33
11	4807	33
12	5324	33

prune5.0ms (0.1%)

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

Error

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 PI.f64)))

Status

Error

Program

▶

0.1b

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

0.5b

(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 PI.f64)))

Compiler

Compiled 205 to 119 computations (42% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite310.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

119×	`add-exp-log_binary64`
76×	`prod-exp_binary64`
75×	`add-cbrt-cube_binary64`
48×	`associate-l_binary64`
46×	`add-sqr-sqrt_binary64`

Counts

4 → 177

Calls

4 calls:

33.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
30.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
15.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 14265 to 4867 computations (65.9% saved)

series80.0ms (1.1%)

Error

0.0b

Counts

4 → 9

Calls

4 calls:

49.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
13.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
12.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1079 to 618 computations (42.7% saved)

simplify185.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

565×	`associate-r_binary64`
467×	`associate-l_binary64`
373×	`unswap-sqr_binary64`
325×	`fma-neg_binary64`
228×	`*-commutative_binary64`

Counts

186 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	7899
1	952	6258
2	3795	5188
3	4996	5188

prune151.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	162	6	168

Error

Counts

168 → 6

Alt Table

Status	Error	Program
	42.1b	(fabs.f64 (/.f64 (fma.f64 21 (fma.f64 5 (fma.f64 8/27 (pow.f64 (pow.f64 (fabs.f64 x) 3) 3) (.f64 (pow.f64 (fabs.f64 x) 3) 8)) (.f64 (pow.f64 (fabs.f64 x) 5) (fma.f64 4 (.f64 x x) (fma.f64 (pow.f64 (fabs.f64 x) 6) 4/9 (.f64 -2 (.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))))) (.f64 (pow.f64 (fabs.f64 x) 7) (.f64 5 (fma.f64 4 (.f64 x x) (fma.f64 (pow.f64 (fabs.f64 x) 6) 4/9 (.f64 -2 (.f64 (pow.f64 (fabs.f64 x) 4) 2/3))))))) (.f64 (sqrt.f64 PI.f64) (.f64 (fma.f64 4 (.f64 x x) (fma.f64 (pow.f64 (fabs.f64 x) 6) 4/9 (.f64 -2 (*.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))) 105))))
▶	0.3b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 PI.f64)))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))))
	0.5b	(fabs.f64 (+.f64 (/.f64 (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3)))) (sqrt.f64 PI.f64)) (.f64 (pow.f64 (fabs.f64 x) 7) (/.f64 1/21 (sqrt.f64 PI.f64)))))
	31.1b	(fabs.f64 (/.f64 (fma.f64 (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3)))) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3)))) (.f64 -1/441 (.f64 (.f64 x x) (pow.f64 (fabs.f64 x) 12)))) (.f64 (sqrt.f64 PI.f64) (-.f64 (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3)))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))))))

Compiler

Compiled 6628 to 3306 computations (50.1% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 PI.f64)))
0.3b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 PI.f64))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite269.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

157×	`add-sqr-sqrt_binary64`
141×	`sqrt-prod_binary64`
126×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
66×	`add-cube-cbrt_binary64`

Counts

4 → 199

Calls

4 calls:

25.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 PI.f64))))
5.0ms	(/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 PI.f64)))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 7802 to 4567 computations (41.5% saved)

series101.0ms (1.4%)

Error

Counts

4 → 6

Calls

4 calls:

52.0ms	(/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 PI.f64)))
45.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 PI.f64))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 496 to 389 computations (21.6% saved)

simplify307.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

724×	`distribute-rgt-in_binary64`
723×	`distribute-lft-in_binary64`
326×	`times-frac_binary64`
133×	`associate-r_binary64`
119×	`fma-def_binary64`

Counts

205 → 177

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	182	12363
1	411	11138
2	1299	11138
3	4999	11138
4	4966	11138

prune148.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	179	4	183

Error

Counts

183 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))))
▶	0.4b	(fabs.f64 (.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (fabs.f64 (cbrt.f64 PI.f64)))) (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 PI.f64))))))
	0.5b	(fabs.f64 (+.f64 (/.f64 (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3)))) (sqrt.f64 PI.f64)) (.f64 (pow.f64 (fabs.f64 x) 7) (/.f64 1/21 (sqrt.f64 PI.f64)))))

Compiler

Compiled 5009 to 2957 computations (41% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 PI.f64))))
1.0b	(cbrt.f64 PI.f64)
1.0b	(cbrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite167.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

63×	`sqrt-prod_binary64`
37×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`

Counts

4 → 106

Calls

4 calls:

7.0ms	(/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 PI.f64))))
4.0ms	(cbrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)

Compiler

Compiled 5248 to 2867 computations (45.4% saved)

series57.0ms (0.8%)

Error

Counts

4 → 3

Calls

4 calls:

55.0ms	(/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 PI.f64))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)

Compiler

Compiled 308 to 245 computations (20.5% saved)

simplify183.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

771×	`fma-def_binary64`
536×	`associate-*l/_binary64`
389×	`associate-/l*_binary64`
352×	`times-frac_binary64`
267×	`distribute-rgt-in_binary64`

Counts

109 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	5220
1	240	5045
2	557	5036
3	2077	4828
4	4708	4828
5	5038	4828

prune68.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	73	4	77

Error

Counts

77 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
▶	0.5b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))))
✓	0.4b	(fabs.f64 (.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (fabs.f64 (cbrt.f64 PI.f64)))) (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 PI.f64))))))
	0.5b	(fabs.f64 (+.f64 (/.f64 (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3)))) (sqrt.f64 PI.f64)) (.f64 (pow.f64 (fabs.f64 x) 7) (/.f64 1/21 (sqrt.f64 PI.f64)))))

Compiler

Compiled 2940 to 1528 computations (48% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))
0.3b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64)))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite214.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

75×	`sqrt-prod_binary64`
51×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`

Counts

4 → 123

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64)))))
11.0ms	(.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 4855 to 3196 computations (34.2% saved)

series103.0ms (1.4%)

Error

Counts

4 → 6

Calls

4 calls:

52.0ms	(.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))
48.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64)))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 496 to 389 computations (21.6% saved)

simplify279.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

683×	`unswap-sqr_binary64`
435×	`sqr-pow_binary64`
289×	`associate-*l/_binary64`
265×	`fma-def_binary64`
237×	`associate-/l*_binary64`

Counts

129 → 101

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	129	5799
1	245	5065
2	760	4990
3	1163	4780
4	2350	4765
5	2582	4765
6	4134	4765
7	4939	4765
8	5091	4765

prune112.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	101	4	105

Error

Counts

105 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
✓	0.5b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))))
✓	0.4b	(fabs.f64 (.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (fabs.f64 (cbrt.f64 PI.f64)))) (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 PI.f64))))))
	0.5b	(fabs.f64 (+.f64 (/.f64 (fma.f64 1/5 (pow.f64 (fabs.f64 x) 5) (fma.f64 2 (fabs.f64 x) (.f64 2/3 (pow.f64 (fabs.f64 x) 3)))) (sqrt.f64 PI.f64)) (.f64 (pow.f64 (fabs.f64 x) 7) (/.f64 1/21 (sqrt.f64 PI.f64)))))

Compiler

Compiled 3044 to 1927 computations (36.7% saved)

regimes2.6s (34.9%)

Accuracy

Total 0.1b remaining (70.7%)

Threshold costs 0.1b (70.7%)

Compiler

Compiled 59860 to 40197 computations (32.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`fabs-mul_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	44
1	30	44
2	31	44
3	30	44

end1.0ms (0%)

Compiler: Compiled 29 to 22 computations (24.1% saved)

sample1.7s (22.7%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
116.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 276 to 166 computations (39.9% saved)

Details

analyze125.0ms (1.7%)

sample45.0ms (0.6%)

simplify114.0ms (1.6%)

prune5.0ms (0.1%)

localize27.0ms (0.4%)

rewrite310.0ms (4.2%)

series80.0ms (1.1%)

simplify185.0ms (2.5%)

prune151.0ms (2.1%)

localize18.0ms (0.3%)

rewrite269.0ms (3.7%)

series101.0ms (1.4%)

simplify307.0ms (4.2%)

prune148.0ms (2%)

localize24.0ms (0.3%)

rewrite167.0ms (2.3%)

series57.0ms (0.8%)

simplify183.0ms (2.5%)

prune68.0ms (0.9%)

localize18.0ms (0.2%)

rewrite214.0ms (2.9%)

series103.0ms (1.4%)

simplify279.0ms (3.8%)

prune112.0ms (1.5%)

regimes2.6s (34.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.7s (22.7%)

Profiling