Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
74.9%	0%	25.1%	1

Compiler

Compiled 71 to 33 computations (53.5% saved)

sample2.6s (34.7%)

Results

2.4s

8256×

body

128

valid

Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify135.0ms (1.8%)

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 → 2

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

prune11.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(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))))
▶	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))))))

Status

Error

Program

0.3b

(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))))

▶

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))))))

Compiler

Compiled 272 to 147 computations (46% saved)

localize51.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
✓	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 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	1.0b	(sqrt.f64 (PI.f64))

series178.0ms (2.4%)

Counts

4 → 36

Calls

4 calls:

145.0ms	(.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)))))
19.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
14.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite140.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
39×	`add-exp-log_binary64`
38×	`add-cbrt-cube_binary64`
36×	`associate-l_binary64`
35×	`pow1_binary64`

Counts

4 → 155

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)))))
21.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
14.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
5.0ms	(sqrt.f64 (PI.f64))

simplify274.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

519×	`associate-r_binary64`
418×	`associate-l_binary64`
389×	`cancel-sign-sub-inv_binary64`
313×	`fma-neg_binary64`
213×	`*-commutative_binary64`

Counts

191 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	286	7308
1	870	5784
2	3510	5032
3	4912	5032

prune687.0ms (9.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	304	4	308
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	305	5	310

Error

Counts

310 → 5

Alt Table

Status	Error	Program
	1.1b	(fabs.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (PI.f64))))) (.f64 (cbrt.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)))))))
	4.0b	(fabs.f64 (exp.f64 (log.f64 (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64))))))
	0.3b	(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))))
▶	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
	0.3b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))))))

Compiler

Compiled 24441 to 9279 computations (62% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))
✓	0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
✓	0.1b	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
✓	0.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))

series214.0ms (2.9%)

Counts

4 → 36

Calls

4 calls:

90.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
56.0ms	(fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))
38.0ms	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
30.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
19×	`associate-l_binary64`
18×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 92

Calls

4 calls:

8.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
7.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
0.0ms	(fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))
0.0ms	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

simplify127.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

618×	`distribute-rgt-in_binary64`
617×	`distribute-lft-in_binary64`
600×	`associate-+l+_binary64`
529×	`associate-l_binary64`
453×	`associate-r_binary64`

Counts

128 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	4283
1	265	4015
2	813	4003
3	3517	4003
4	5634	4003

prune206.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	114	5	119

Error

Counts

119 → 5

Alt Table

Status	Error	Program
	1.1b	(fabs.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (PI.f64))))) (.f64 (cbrt.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)))))))
	4.0b	(fabs.f64 (exp.f64 (log.f64 (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64))))))
	0.3b	(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))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
▶	0.3b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))))))

Compiler

Compiled 4723 to 3252 computations (31.1% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
✓	0.1b	(.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))))
✓	0.2b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (PI.f64))))))
	1.0b	(sqrt.f64 (PI.f64))

series656.0ms (8.9%)

Counts

2 → 24

Calls

2 calls:

536.0ms

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

120.0ms

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

rewrite71.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`sqrt-prod_binary64`
45×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`

Counts

2 → 93

Calls

2 calls:

28.0ms

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

16.0ms

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

simplify370.0ms (5%)

Algorithm

1×	egg-herbie

Rules

804×	`unswap-sqr_binary64`
473×	`fma-def_binary64`
298×	`associate-*l/_binary64`
249×	`*-commutative_binary64`
249×	`sqr-pow_binary64`

Counts

117 → 138

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	118	6188
1	232	5599
2	887	5557
3	1352	5311
4	2635	5311
5	3105	5236
6	4667	5236
7	4951	5236

prune432.0ms (5.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	182	5	187

Error

Counts

187 → 5

Alt Table

Status	Error	Program
	1.1b	(fabs.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (PI.f64))))) (.f64 (cbrt.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)))))))
▶	0.3b	(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))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
	4.1b	(fabs.f64 (exp.f64 (log.f64 (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (sqrt.f64 (PI.f64))))))
✓	0.3b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))) (.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (PI.f64)))))))

Compiler

Compiled 8482 to 5502 computations (35.1% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
✓	0.1b	(*.f64 2/3 (pow.f64 x 3))
✓	0.2b	(/.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)))
	1.0b	(sqrt.f64 (PI.f64))

series29.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

15.0ms

(/.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)))

7.0ms

(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))

6.0ms

(*.f64 2/3 (pow.f64 x 3))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
12×	`associate-r_binary64`

Counts

3 → 84

Calls

3 calls:

9.0ms

(*.f64 2/3 (pow.f64 x 3))

5.0ms

(/.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)))

1.0ms

(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))

simplify151.0ms (2%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-l_binary64`
610×	`associate-r_binary64`
285×	`log-prod_binary64`
262×	`fma-def_binary64`
184×	`swap-sqr_binary64`

Counts

108 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	3342
1	305	3139
2	796	3025
3	3438	3025
4	4851	3025
5	4876	3025

prune219.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	0	2
Picked	0	1	1
Done	1	1	2
Total	132	4	136

Error

Counts

136 → 4

Alt Table

Status	Error	Program
	0.9b	(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))))) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
✓	0.3b	(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))))
	0.3b	(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))))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))))

Compiler

Compiled 4169 to 3068 computations (26.4% saved)

regimes496.0ms (6.7%)

Accuracy

Total 0.1b remaining (98.7%)

Threshold costs 0.1b (98.7%)

Counts

51 → 1

Compiler

Compiled 9633 to 6636 computations (31.1% saved)

simplify6.0ms (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

end244.0ms (3.3%)

Compiler: Compiled 163 to 127 computations (22.1% saved)

Details

analyze2.0ms (0%)

sample2.6s (34.7%)

simplify135.0ms (1.8%)

prune11.0ms (0.1%)

localize51.0ms (0.7%)

series178.0ms (2.4%)

rewrite140.0ms (1.9%)

simplify274.0ms (3.7%)

prune687.0ms (9.3%)

localize22.0ms (0.3%)

series214.0ms (2.9%)

rewrite22.0ms (0.3%)

simplify127.0ms (1.7%)

prune206.0ms (2.8%)

localize20.0ms (0.3%)

series656.0ms (8.9%)

rewrite71.0ms (1%)

simplify370.0ms (5%)

prune432.0ms (5.9%)

localize29.0ms (0.4%)

series29.0ms (0.4%)

rewrite26.0ms (0.4%)

simplify151.0ms (2%)

prune219.0ms (3%)

regimes496.0ms (6.7%)

simplify6.0ms (0.1%)

end244.0ms (3.3%)

Profiling