Details

analyze5.0ms (0.2%)

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)

sample140.0ms (4%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify94.0ms (2.7%)

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

prune5.0ms (0.2%)

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
	0.5b	(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))))
▶	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

0.5b

(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))))

▶

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)

localize21.0ms (0.6%)

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))

series91.0ms (2.6%)

Counts

4 → 36

Calls

4 calls:

75.0ms	(.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)))))
10.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite61.0ms (1.8%)

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:

23.0ms	(.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)))))
9.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 (PI.f64))

simplify144.0ms (4.1%)

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

prune352.0ms (10.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	308	2	310

Error

Counts

310 → 2

Alt Table

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

Status

Error

Program

0.5b

(fabs.f64 (+.f64 (/.f64 (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))) (/.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (sqrt.f64 (PI.f64)))))

▶

0.1b

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

Compiler

Compiled 24171 to 9113 computations (62.3% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series122.0ms (3.5%)

Counts

4 → 0

Calls

4 calls:

78.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
18.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
16.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
10.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

rewrite46.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
45×	`associate-r_binary64`
30×	`unpow-prod-down_binary64`
28×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`

Counts

4 → 154

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 2 (fabs.f64 x)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
5.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
5.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))

simplify109.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-def_binary64`
418×	`fma-neg_binary64`
261×	`associate-l_binary64`
244×	`associate-r_binary64`
199×	`associate-+r+_binary64`

Counts

154 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	3894
1	602	3642
2	2070	2958
3	4180	2958
4	4888	2958

prune271.0ms (7.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	229	2	231

Error

Counts

231 → 2

Alt Table

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

Status

Error

Program

▶

0.5b

(fabs.f64 (+.f64 (/.f64 (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))) (/.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (sqrt.f64 (PI.f64)))))

✓

0.1b

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

Compiler

Compiled 9318 to 6745 computations (27.6% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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)))
✓	0.3b	(/.f64 (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)))
	1.0b	(sqrt.f64 (PI.f64))

series76.0ms (2.2%)

Counts

2 → 24

Calls

2 calls:

49.0ms

(/.f64 (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)))

26.0ms

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

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
12×	`sqrt-prod_binary64`

Counts

2 → 51

Calls

2 calls:

3.0ms

(/.f64 (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)))

0.0ms

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

simplify97.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

849×	`distribute-rgt-in_binary64`
838×	`distribute-lft-in_binary64`
759×	`times-frac_binary64`
714×	`fma-def_binary64`
146×	`fma-neg_binary64`

Counts

75 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	2912
1	153	2753
2	407	2753
3	1321	2611
4	4818	2611
5	5616	2611

prune187.0ms (5.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	160	2	162

Error

Counts

162 → 2

Alt Table

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

Status

Error

Program

✓

0.5b

(fabs.f64 (+.f64 (/.f64 (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))) (/.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (sqrt.f64 (PI.f64)))))

✓

0.1b

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

Compiler

Compiled 6416 to 3873 computations (39.6% saved)

regimes161.0ms (4.6%)

Accuracy

Total 0.1b remaining (84.2%)

Threshold costs 0.1b (84.2%)

Counts

20 → 1

Compiler

Compiled 3604 to 2548 computations (29.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`fabs-mul_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	50
1	39	50
2	40	50
3	39	50

end1.0ms (0%)

Compiler: Compiled 32 to 25 computations (21.9% saved)

sample1.5s (41.7%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
104.0ms	8003×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 167 to 106 computations (36.5% saved)

Details

analyze5.0ms (0.2%)

sample140.0ms (4%)

simplify94.0ms (2.7%)

prune5.0ms (0.2%)

localize21.0ms (0.6%)

series91.0ms (2.6%)

rewrite61.0ms (1.8%)

simplify144.0ms (4.1%)

prune352.0ms (10.1%)

localize17.0ms (0.5%)

series122.0ms (3.5%)

rewrite46.0ms (1.3%)

simplify109.0ms (3.1%)

prune271.0ms (7.8%)

localize15.0ms (0.4%)

series76.0ms (2.2%)

rewrite7.0ms (0.2%)

simplify97.0ms (2.8%)

prune187.0ms (5.4%)

regimes161.0ms (4.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.5s (41.7%)

Profiling