Details

analyze8.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.2s (43.9%)

Results

1.1s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify118.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1332×	`fma-def_binary64`
889×	`associate-/r*_binary64`
605×	`neg-sub0_binary64`
599×	`neg-mul-1_binary64`
576×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	42	28
2	102	26
3	261	26
4	684	26
5	1088	24
6	1801	24
7	3541	24
8	3914	24
9	4002	24
10	4416	24
11	4409	24
12	4415	24
13	5159	24

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
▶	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Status

Error

Program

▶

0.0b

(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

1.0b

(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))

Compiler

Compiled 113 to 85 computations (24.8% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (PI.f64) (fma.f64 v v -1))
✓	0.0b	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
✓	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series17.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
6.0ms	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
5.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 60

Calls

3 calls:

3.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
3.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))
1.0ms	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))

simplify96.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

471×	`associate-/r*_binary64`
371×	`associate-l_binary64`
322×	`associate-r_binary64`
304×	`fma-def_binary64`
273×	`times-frac_binary64`

Counts

96 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	1691
1	445	1508
2	1390	1488
3	4655	1488
4	4945	1488
5	4918	1488

prune86.0ms (3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	113	3	116

Error

Counts

116 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
▶	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))
	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Compiler

Compiled 2764 to 2004 computations (27.5% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) (cbrt.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
	0.0b	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
✓	0.0b	(cbrt.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series15.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

8.0ms

(cbrt.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

7.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (cbrt.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) (cbrt.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64`
14×	`cbrt-prod_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`pow1/3_binary64`
9×	`associate-r_binary64`

Counts

2 → 58

Calls

2 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (cbrt.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) (cbrt.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))

1.0ms

(cbrt.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

simplify79.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-neg_binary64`
357×	`associate-l_binary64`
340×	`associate-r_binary64`
309×	`fma-def_binary64`
252×	`associate-/r*_binary64`

Counts

82 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	1997
1	423	1923
2	1188	1584
3	4215	1516
4	4903	1516

prune454.0ms (16%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	349	0	349
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	349	3	352

Error

Counts

352 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
✓	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))
▶	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Compiler

Compiled 15414 to 11946 computations (22.5% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))
✓	0.0b	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
✓	0.2b	(.f64 6 (.f64 v v))
✓	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

series54.0ms (1.9%)

Counts

4 → 48

Calls

4 calls:

27.0ms	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
17.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
7.0ms	(sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))
3.0ms	(.f64 6 (.f64 v v))

rewrite38.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
19×	`pow1_binary64`
16×	`associate-*r/_binary64`
15×	`cbrt-unprod_binary64`

Counts

4 → 107

Calls

4 calls:

10.0ms	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
10.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
5.0ms	(.f64 6 (.f64 v v))
3.0ms	(sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))

simplify148.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

401×	`associate-l_binary64`
387×	`associate-r_binary64`
378×	`fma-neg_binary64`
290×	`associate-/r*_binary64`
228×	`fma-def_binary64`

Counts

155 → 237

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	420	5211
1	1202	4683
2	4875	4683
3	5128	4683

prune203.0ms (7.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	237	3	240

Error

Counts

240 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
✓	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))
✓	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Compiler

Compiled 8381 to 5995 computations (28.5% saved)

regimes131.0ms (4.6%)

Accuracy

Total 0.0b remaining (62.4%)

Threshold costs 0.0b (62.4%)

Counts

25 → 1

Compiler

Compiled 2578 to 2036 computations (21% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	16	24
2	16	24

end84.0ms (3%)

Compiler: Compiled 108 to 83 computations (23.1% saved)

Details

analyze8.0ms (0.3%)

sample1.2s (43.9%)

simplify118.0ms (4.1%)

prune5.0ms (0.2%)

localize11.0ms (0.4%)

series17.0ms (0.6%)

rewrite9.0ms (0.3%)

simplify96.0ms (3.4%)

prune86.0ms (3%)

localize14.0ms (0.5%)

series15.0ms (0.5%)

rewrite14.0ms (0.5%)

simplify79.0ms (2.8%)

prune454.0ms (16%)

localize11.0ms (0.4%)

series54.0ms (1.9%)

rewrite38.0ms (1.3%)

simplify148.0ms (5.2%)

prune203.0ms (7.1%)

regimes131.0ms (4.6%)

simplify3.0ms (0.1%)

end84.0ms (3%)

Profiling