Details

analyze135.0ms (2.4%)

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)

sample46.0ms (0.8%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify101.0ms (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

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
▶	0.1b	(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 272 to 147 computations (46% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.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 (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))

series41.0ms (0.7%)

Counts

4 → 36

Calls

4 calls:

23.0ms	(.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)))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite121.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

177×	`add-exp-log_binary64`
127×	`prod-exp_binary64`
110×	`add-cbrt-cube_binary64`
71×	`cbrt-unprod_binary64`
68×	`pow1_binary64`

Counts

4 → 167

Calls

4 calls:

69.0ms	(.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 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 (PI.f64))

simplify130.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

773×	`fma-def_binary64`
524×	`unswap-sqr_binary64`
377×	`associate-r_binary64`
368×	`associate-l_binary64`
208×	`associate-/l*_binary64`

Counts

203 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	254	3528
1	460	2265
2	1531	1948
3	3663	1918
4	4711	1918
5	5116	1918

prune404.0ms (7.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	293	1	294
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	294	2	296

Error

0.0b

Counts

296 → 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))))
	0.8b	(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 (cbrt.f64 (pow.f64 (fabs.f64 x) 9)) (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))))

0.8b

(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 (cbrt.f64 (pow.f64 (fabs.f64 x) 9)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 21363 to 7600 computations (64.4% saved)

localize14.0ms (0.2%)

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))

series18.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

11.0ms

(/.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)))

4.0ms

(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)))))

3.0ms

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

rewrite20.0ms (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:

11.0ms

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

3.0ms

(/.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)))

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)))))

simplify127.0ms (2.3%)

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 → 145

Iterations

Useful iterations: 2 (0.0ms)

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

prune245.0ms (4.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	160	3	163

Error

Counts

163 → 3

Alt Table

Status	Error	Program
	0.8b	(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 (cbrt.f64 (pow.f64 (fabs.f64 x) 9)) (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))))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))))
✓	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 5321 to 3876 computations (27.2% saved)

localize16.0ms (0.3%)

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))))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))))
	1.0b	(sqrt.f64 (PI.f64))

series9.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(/.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))))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
3×	`associate-/l*_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`

Counts

1 → 23

Calls

1 calls:

10.0ms

(/.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))))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
634×	`distribute-rgt-in_binary64`
628×	`distribute-lft-in_binary64`
529×	`times-frac_binary64`
186×	`associate-/l/_binary64`

Counts

35 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	1530
1	183	1341
2	472	1239
3	1392	1183
4	4932	1183
5	5330	1183

prune202.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	148	3	151

Error

Counts

151 → 3

Alt Table

Status	Error	Program
▶	0.8b	(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 (cbrt.f64 (pow.f64 (fabs.f64 x) 9)) (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))))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))))
✓	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 5069 to 3292 computations (35.1% saved)

localize32.0ms (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 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
	1.0b	(sqrt.f64 (PI.f64))
✓	13.3b	(cbrt.f64 (pow.f64 (fabs.f64 x) 9))

series7.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

7.0ms

(cbrt.f64 (pow.f64 (fabs.f64 x) 9))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`cbrt-prod_binary64`
7×	`unpow-prod-down_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 21

Calls

1 calls:

2.0ms

(cbrt.f64 (pow.f64 (fabs.f64 x) 9))

simplify135.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1211×	`sqr-pow_binary64`
862×	`fabs-mul_binary64`
646×	`cube-prod_binary64`
468×	`pow-sqr_binary64`
406×	`associate-l_binary64`

Counts

33 → 25

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	373
1	82	373
2	116	365
3	193	365
4	392	365
5	969	365
6	1106	365
7	1384	365
8	1779	365
9	2400	365
10	3272	365
11	3601	365
12	3863	365
13	3878	365
14	3998	365
15	4122	365
16	5426	365

prune344.0ms (6.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	188	3	191

Error

Counts

191 → 3

Alt Table

Status	Error	Program
✓	0.8b	(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 (cbrt.f64 (pow.f64 (fabs.f64 x) 9)) (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))))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))))
✓	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 12943 to 6107 computations (52.8% saved)

regimes1.5s (26.9%)

Accuracy

Total 0.1b remaining (77.8%)

Threshold costs 0.1b (77.8%)

Counts

162 → 1

Compiler

Compiled 37769 to 24453 computations (35.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	33	76
1	50	76
2	54	76
3	50	76

end1.0ms (0%)

Compiler: Compiled 48 to 31 computations (35.4% saved)

sample1.8s (32.3%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
141.0ms	8000×	pre	128	true

Compiler

Compiled 236 to 141 computations (40.3% saved)

Details

analyze135.0ms (2.4%)

sample46.0ms (0.8%)

simplify101.0ms (1.8%)

prune6.0ms (0.1%)

localize26.0ms (0.5%)

series41.0ms (0.7%)

rewrite121.0ms (2.2%)

simplify130.0ms (2.3%)

prune404.0ms (7.3%)

localize14.0ms (0.2%)

series18.0ms (0.3%)

rewrite20.0ms (0.4%)

simplify127.0ms (2.3%)

prune245.0ms (4.4%)

localize16.0ms (0.3%)

series9.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify71.0ms (1.3%)

prune202.0ms (3.6%)

localize32.0ms (0.6%)

series7.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify135.0ms (2.4%)

prune344.0ms (6.2%)

regimes1.5s (26.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.8s (32.3%)

Profiling