Details

analyze136.0ms (1.4%)

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)

sample49.0ms (0.5%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify111.0ms (1.1%)

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

prune6.0ms (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
	0.5b	(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)

localize27.0ms (0.3%)

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 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)

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`add-exp-log_binary64`
78×	`add-cbrt-cube_binary64`
75×	`prod-exp_binary64`
53×	`pow1_binary64`
45×	`cbrt-unprod_binary64`

Counts

4 → 153

Calls

4 calls:

25.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (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)))
8.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)

series62.0ms (0.6%)

Counts

4 → 36

Calls

4 calls:

28.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (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)))
12.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify153.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

504×	`associate-/l*_binary64`
471×	`fma-def_binary64`
345×	`associate-/r*_binary64`
331×	`unswap-sqr_binary64`
310×	`associate-r_binary64`

Counts

189 → 317

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	217	2646
1	396	2039
2	1372	1782
3	2977	1752
4	4619	1719
5	4996	1719
6	4891	1719

prune269.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	316	1	317
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	316	3	319

Error

Counts

319 → 3

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))))))
	1.1b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (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 14229 to 5123 computations (64% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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)))))
✓	0.1b	(*.f64 2/3 (pow.f64 x 3))
✓	0.3b	(/.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)

rewrite14.0ms (0.1%)

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:

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))

5.0ms

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

0.0ms

(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)))))

series37.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

14.0ms

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

14.0ms

(/.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))

9.0ms

(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)))))

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-l_binary64`
599×	`associate-r_binary64`
300×	`fma-def_binary64`
205×	`cancel-sign-sub-inv_binary64`
199×	`exp-prod_binary64`

Counts

108 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3453
1	317	3236
2	795	3122
3	3459	3122
4	4864	3122

prune270.0ms (2.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	213	3	216

Error

Counts

216 → 3

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))))))
▶	0.4b	(fabs.f64 (/.f64 (/.f64 (fma.f64 1/5 (pow.f64 x 5) (fma.f64 1/21 (pow.f64 x 7) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (fabs.f64 (cbrt.f64 PI.f64))) (sqrt.f64 (cbrt.f64 PI.f64))))

Compiler

Compiled 5237 to 3821 computations (27% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (/.f64 (fma.f64 1/5 (pow.f64 x 5) (fma.f64 1/21 (pow.f64 x 7) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (fabs.f64 (cbrt.f64 PI.f64))) (sqrt.f64 (cbrt.f64 PI.f64)))
✓	0.4b	(/.f64 (fma.f64 1/5 (pow.f64 x 5) (fma.f64 1/21 (pow.f64 x 7) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (fabs.f64 (cbrt.f64 PI.f64)))
	1.0b	(cbrt.f64 PI.f64)
✓	1.0b	(cbrt.f64 PI.f64)

rewrite74.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

696×	`times-frac_binary64`
420×	`add-sqr-sqrt_binary64`
352×	`*-un-lft-identity_binary64`
352×	`add-cube-cbrt_binary64`
253×	`cbrt-prod_binary64`

Counts

3 → 470

Calls

3 calls:

15.0ms

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

4.0ms

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

1.0ms

(cbrt.f64 PI.f64)

series41.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

25.0ms

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

16.0ms

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

0.0ms

(cbrt.f64 PI.f64)

simplify876.0ms (8.9%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-def_binary64`
858×	`times-frac_binary64`
589×	`associate-/l*_binary64`
319×	`associate-l_binary64`
309×	`associate-/r*_binary64`

Counts

494 → 961

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	513	37179
1	1141	34932
2	1799	34267
3	4530	34261
4	5208	34261

prune1.2s (12.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	978	0	978
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	978	3	981

Error

Counts

981 → 3

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))))))
✓	0.4b	(fabs.f64 (/.f64 (/.f64 (fma.f64 1/5 (pow.f64 x 5) (fma.f64 1/21 (pow.f64 x 7) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (fabs.f64 (cbrt.f64 PI.f64))) (sqrt.f64 (cbrt.f64 PI.f64))))

Compiler

Compiled 37354 to 24396 computations (34.7% saved)

regimes4.8s (49.2%)

Accuracy

Total 0.1b remaining (85.9%)

Threshold costs 0.1b (85.9%)

Compiler

Compiled 111677 to 80360 computations (28% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`fabs-mul_binary64`
1×	`sqr-abs_binary64`
1×	`fabs-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	86
1	53	86
2	57	86
3	52	86

end1.0ms (0%)

Compiler: Compiled 54 to 28 computations (48.1% saved)

sample1.4s (14.6%)

Algorithm

1×

intervals

Results

953.0ms	8000×	body	128	valid
101.0ms	8003×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 245 to 134 computations (45.3% saved)

Details

analyze136.0ms (1.4%)

sample49.0ms (0.5%)

simplify111.0ms (1.1%)

prune6.0ms (0.1%)

localize27.0ms (0.3%)

rewrite53.0ms (0.5%)

series62.0ms (0.6%)

simplify153.0ms (1.6%)

prune269.0ms (2.7%)

localize14.0ms (0.1%)

rewrite14.0ms (0.1%)

series37.0ms (0.4%)

simplify114.0ms (1.2%)

prune270.0ms (2.7%)

localize17.0ms (0.2%)

rewrite74.0ms (0.7%)

series41.0ms (0.4%)

simplify876.0ms (8.9%)

prune1.2s (12.5%)

regimes4.8s (49.2%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.4s (14.6%)

Profiling