Details

analyze158.0ms (2.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 31 to 22 computations (29% saved)

sample1.3s (17.1%)

Results

1.2s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 92 to 65 computations (29.3% saved)

simplify32.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
592×	`fma-def_binary64`
509×	`associate-/r*_binary64`
353×	`associate-/l*_binary64`
343×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	58	43
2	179	38
3	824	36
4	3882	36
5	5029	36

prune4.0ms (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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.6b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
▶	0.6b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))

Status

Error

Program

0.6b

(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))

▶

0.6b

(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))

Compiler

Compiled 166 to 115 computations (30.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 5 (.f64 v v))
✓	0.3b	(*.f64 (PI.f64) t)
✓	0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
✓	0.5b	(.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

series206.0ms (2.7%)

Counts

4 → 60

Calls

4 calls:

165.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
35.0ms	(.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
4.0ms	(.f64 5 (.f64 v v))
2.0ms	(*.f64 (PI.f64) t)

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
18×	`associate-*r/_binary64`
16×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
7.0ms	(.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
4.0ms	(.f64 5 (.f64 v v))
3.0ms	(*.f64 (PI.f64) t)

simplify126.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-l_binary64`
489×	`associate-r_binary64`
436×	`times-frac_binary64`
397×	`associate-/r*_binary64`
215×	`associate-/l*_binary64`

Counts

162 → 195

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	339	5940
1	1042	5332
2	4928	5332
3	4937	5332

prune272.0ms (3.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	186	9	195
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	187	10	197

Error

0.3b

Counts

197 → 10

Alt Table

Status	Error	Program
	1.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) t)) (cbrt.f64 (.f64 (PI.f64) t))) (cbrt.f64 (.f64 (PI.f64) t))) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
	0.7b	(-.f64 (/.f64 1 (.f64 (PI.f64) (.f64 t (sqrt.f64 2)))) (.f64 5/2 (/.f64 (pow.f64 v 2) (.f64 (PI.f64) (*.f64 t (sqrt.f64 2))))))
	0.8b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) t)) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))
	0.6b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
	35.3b	(.f64 (sqrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))) (sqrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
	40.3b	(cbrt.f64 (/.f64 (.f64 (.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 1 (.f64 5 (.f64 v v)))) (.f64 (.f64 (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (PI.f64)) (.f64 (.f64 t t) t)) (.f64 (.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (.f64 (.f64 (-.f64 1 (.f64 v v)) (-.f64 1 (.f64 v v))) (-.f64 1 (*.f64 v v))))))
	40.3b	(cbrt.f64 (/.f64 (.f64 (.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 1 (.f64 5 (.f64 v v)))) (.f64 (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
	1.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
	35.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (-.f64 1 (*.f64 v v))))
▶	0.5b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))) t)) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))

Compiler

Compiled 9537 to 6224 computations (34.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 5 (pow.f64 v 2))
✓	0.2b	(.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))
✓	0.2b	(.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))) t)
✓	0.5b	(/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (*.f64 (PI.f64) (sqrt.f64 2)))) t))

series151.0ms (2%)

Counts

4 → 24

Calls

4 calls:

109.0ms	(/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (*.f64 (PI.f64) (sqrt.f64 2)))) t))
32.0ms	(.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))) t)
8.0ms	(.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))
3.0ms	(*.f64 5 (pow.f64 v 2))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`
14×	`associate-l_binary64`
14×	`prod-exp_binary64`

Counts

4 → 106

Calls

4 calls:

8.0ms	(/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (*.f64 (PI.f64) (sqrt.f64 2)))) t))
7.0ms	(.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))
6.0ms	(.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))) t)
4.0ms	(*.f64 5 (pow.f64 v 2))

simplify225.0ms (3%)

Algorithm

1×	egg-herbie

Rules

405×	`fma-def_binary64`
291×	`distribute-rgt-in_binary64`
268×	`cancel-sign-sub-inv_binary64`
264×	`distribute-lft-in_binary64`
243×	`distribute-rgt-neg-in_binary64`

Counts

130 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	3696
1	543	2941
2	2024	2779
3	4704	2779
4	4953	2779

prune375.0ms (5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	194	5	199

Error

0.0b

Counts

199 → 5

Alt Table

Status	Error	Program
	0.7b	(-.f64 (/.f64 1 (.f64 (PI.f64) (.f64 t (sqrt.f64 2)))) (.f64 5/2 (/.f64 (pow.f64 v 2) (.f64 (PI.f64) (*.f64 t (sqrt.f64 2))))))
	0.5b	(.f64 (.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 t (.f64 (.f64 2 (PI.f64)) (-.f64 (PI.f64) (.f64 (PI.f64) (pow.f64 v 4)))))) (+.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))
▶	0.1b	(.f64 (/.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 (fma.f64 v (neg.f64 v) 1) (.f64 (PI.f64) (sqrt.f64 2)))) t) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))
	0.5b	(.f64 (.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 t (.f64 (+.f64 (neg.f64 (pow.f64 v 6)) 1) (pow.f64 (.f64 (PI.f64) (sqrt.f64 2)) 3)))) (+.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (PI.f64) (sqrt.f64 2))) (+.f64 (.f64 (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2))) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))) (.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2))))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))
	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))) t))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))) t)))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))) t)))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))

Compiler

Compiled 8561 to 6818 computations (20.4% saved)

localize43.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (/.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 (fma.f64 v (neg.f64 v) 1) (.f64 (PI.f64) (sqrt.f64 2)))) t) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))
✓	0.0b	(/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))
✓	0.1b	(/.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2)))) t)
✓	0.1b	(*.f64 3 (pow.f64 v 2))

series276.0ms (3.6%)

Counts

4 → 60

Calls

4 calls:

166.0ms	(.f64 (/.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 (fma.f64 v (neg.f64 v) 1) (.f64 (PI.f64) (sqrt.f64 2)))) t) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))
96.0ms	(/.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2)))) t)
11.0ms	(/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))
3.0ms	(*.f64 3 (pow.f64 v 2))

rewrite76.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`times-frac_binary64`
75×	`add-sqr-sqrt_binary64`
52×	`add-exp-log_binary64`
49×	`*-un-lft-identity_binary64`
49×	`add-cbrt-cube_binary64`

Counts

4 → 181

Calls

4 calls:

38.0ms	(.f64 (/.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 (fma.f64 v (neg.f64 v) 1) (.f64 (PI.f64) (sqrt.f64 2)))) t) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))
7.0ms	(/.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2)))) t)
5.0ms	(/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))
4.0ms	(*.f64 3 (pow.f64 v 2))

simplify233.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

657×	`fma-def_binary64`
371×	`associate-/r*_binary64`
320×	`associate-r_binary64`
284×	`associate-l_binary64`
253×	`*-commutative_binary64`

Counts

241 → 354

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	432	11194
1	1196	9871
2	4313	9664
3	4960	9664

prune538.0ms (7.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	351	3	354
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	354	5	359

Error

Counts

359 → 5

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 t (.f64 (.f64 2 (PI.f64)) (-.f64 (PI.f64) (.f64 (PI.f64) (pow.f64 v 4)))))) (+.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))
▶	0.1b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v))))) (.f64 t (sqrt.f64 (fma.f64 (.f64 v v) -3 1))))
	0.5b	(.f64 (.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 t (.f64 (+.f64 (neg.f64 (pow.f64 v 6)) 1) (pow.f64 (.f64 (PI.f64) (sqrt.f64 2)) 3)))) (+.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (PI.f64) (sqrt.f64 2))) (+.f64 (.f64 (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2))) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2)))) (.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2))))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))
	0.6b	(.f64 (.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (.f64 t (sqrt.f64 2)) (-.f64 1 (.f64 v v))))) (sqrt.f64 (sqrt.f64 (/.f64 1 (fma.f64 (.f64 v v) -3 1))))) (sqrt.f64 (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2)))))))
	0.6b	(.f64 (.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v)))))) (/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v)))))) t)) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))

Compiler

Compiled 16422 to 11707 computations (28.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 t (sqrt.f64 (fma.f64 (.f64 v v) -3 1)))
✓	0.0b	(.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v)))
✓	0.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v)))))
✓	0.1b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v))))) (.f64 t (sqrt.f64 (fma.f64 (.f64 v v) -3 1))))

series200.0ms (2.6%)

Counts

4 → 72

Calls

4 calls:

158.0ms	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v))))) (.f64 t (sqrt.f64 (fma.f64 (.f64 v v) -3 1))))
25.0ms	(.f64 t (sqrt.f64 (fma.f64 (.f64 v v) -3 1)))
9.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v)))))
7.0ms	(.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v)))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-cbrt-cube_binary64`
49×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`

Counts

4 → 137

Calls

4 calls:

10.0ms	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v))))) (.f64 t (sqrt.f64 (fma.f64 (.f64 v v) -3 1))))
9.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v)))))
6.0ms	(.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v)))
4.0ms	(.f64 t (sqrt.f64 (fma.f64 (.f64 v v) -3 1)))

simplify155.0ms (2%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
441×	`associate-/r*_binary64`
403×	`associate-r_binary64`
336×	`associate-l_binary64`
266×	`times-frac_binary64`

Counts

209 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	395	7892
1	1101	6717
2	4496	6702
3	5169	6702

prune339.0ms (4.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	234	3	237
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	238	4	242

Error

Counts

242 → 4

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (.f64 t (.f64 (.f64 2 (PI.f64)) (-.f64 (PI.f64) (.f64 (PI.f64) (pow.f64 v 4)))))) (+.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (pow.f64 v 2) (.f64 (PI.f64) (sqrt.f64 2))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (pow.f64 v 2))))))
	0.3b	(.f64 (/.f64 (/.f64 1 (PI.f64)) t) (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 2) (-.f64 1 (.f64 v v)))) (sqrt.f64 (fma.f64 (*.f64 v v) -3 1))))
	0.3b	(.f64 (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (.f64 (PI.f64) (.f64 (sqrt.f64 2) (-.f64 1 (pow.f64 v 4))))) (/.f64 (fma.f64 v v 1) (sqrt.f64 (fma.f64 (*.f64 v v) -3 1))))
	0.1b	(/.f64 (-.f64 (/.f64 1 (.f64 (PI.f64) (sqrt.f64 2))) (.f64 4 (fma.f64 (/.f64 v (PI.f64)) (/.f64 v (sqrt.f64 2)) (/.f64 (pow.f64 v 4) (.f64 (PI.f64) (sqrt.f64 2)))))) (.f64 t (sqrt.f64 (fma.f64 (*.f64 v v) -3 1))))

Compiler

Compiled 9786 to 6685 computations (31.7% saved)

regimes2.6s (34%)

Accuracy

Total 0.3b remaining (96.5%)

Threshold costs 0.3b (96.5%)

Counts

341 → 1

Compiler

Compiled 71303 to 55785 computations (21.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	56
1	34	56
2	41	56
3	45	56
4	48	56
5	49	56
6	47	56

end133.0ms (1.8%)

Compiler: Compiled 223 to 173 computations (22.4% saved)

Details

analyze158.0ms (2.1%)

sample1.3s (17.1%)

simplify32.0ms (0.4%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

series206.0ms (2.7%)

rewrite39.0ms (0.5%)

simplify126.0ms (1.7%)

prune272.0ms (3.6%)

localize17.0ms (0.2%)

series151.0ms (2%)

rewrite30.0ms (0.4%)

simplify225.0ms (3%)

prune375.0ms (5%)

localize43.0ms (0.6%)

series276.0ms (3.6%)

rewrite76.0ms (1%)

simplify233.0ms (3.1%)

prune538.0ms (7.1%)

localize17.0ms (0.2%)

series200.0ms (2.6%)

rewrite43.0ms (0.6%)

simplify155.0ms (2%)

prune339.0ms (4.5%)

regimes2.6s (34%)

simplify3.0ms (0%)

end133.0ms (1.8%)

Profiling