Details

analyze7.0ms (0.2%)

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 (36.6%)

Results

1.1s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify120.0ms (3.7%)

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

Status

Error

Program

1.0b

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

▶

0.0b

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

Compiler

Compiled 113 to 85 computations (24.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series48.0ms (1.4%)

Counts

4 → 48

Calls

4 calls:

28.0ms	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
7.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
6.0ms	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
6.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
39×	`add-cube-cbrt_binary64`
27×	`sqrt-prod_binary64`

Counts

4 → 134

Calls

4 calls:

8.0ms	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
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))

simplify169.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-def_binary64`
306×	`associate-/r*_binary64`
254×	`sub-neg_binary64`
223×	`fma-neg_binary64`
173×	`associate-r_binary64`

Counts

182 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	386	5649
1	1028	5260
2	3616	5237
3	4798	5236
4	4955	5236

prune196.0ms (5.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	225	2	227
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	227	2	229

Error

Counts

229 → 2

Alt Table

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

Status

Error

Program

0.0b

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

▶

0.0b

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

Compiler

Compiled 6655 to 4972 computations (25.3% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series40.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

29.0ms	(/.f64 (.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
7.0ms	(*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))
4.0ms	(/.f64 -4/3 (fma.f64 v v -1))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-exp-log_binary64`
46×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
35×	`add-cbrt-cube_binary64`
31×	`*-un-lft-identity_binary64`

Counts

3 → 129

Calls

3 calls:

9.0ms	(*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))
9.0ms	(/.f64 (.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
2.0ms	(/.f64 -4/3 (fma.f64 v v -1))

simplify168.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

889×	`fma-def_binary64`
225×	`fma-neg_binary64`
202×	`associate-/r*_binary64`
195×	`associate-/l*_binary64`
181×	`sub-neg_binary64`

Counts

165 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	369	4578
1	1015	4033
2	3608	4016
3	4774	4015
4	4987	4015
5	4920	4015

prune244.0ms (7.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	274	2	276

Error

Counts

276 → 2

Alt Table

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

Status

Error

Program

▶

0.0b

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

✓

0.0b

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

Compiler

Compiled 7995 to 6029 computations (24.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series37.0ms (1.1%)

Counts

2 → 24

Calls

2 calls:

28.0ms	(/.f64 (/.f64 1 (/.f64 (.f64 (PI.f64) (fma.f64 v v -1)) -4/3)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
8.0ms	(/.f64 1 (/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3))

rewrite57.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

399×	`times-frac_binary64`
170×	`*-un-lft-identity_binary64`
170×	`add-sqr-sqrt_binary64`
170×	`add-cube-cbrt_binary64`
81×	`sqrt-prod_binary64`

Counts

2 → 273

Calls

2 calls:

11.0ms	(/.f64 (/.f64 1 (/.f64 (.f64 (PI.f64) (fma.f64 v v -1)) -4/3)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
6.0ms	(/.f64 1 (/.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) -4/3))

simplify356.0ms (10.8%)

Algorithm

1×	egg-herbie

Rules

800×	`fma-def_binary64`
260×	`cancel-sign-sub-inv_binary64`
222×	`associate-/r*_binary64`
190×	`fma-neg_binary64`
160×	`sub-neg_binary64`

Counts

297 → 358

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	374	12367
1	987	11472
2	3247	11191
3	4920	11191
4	4989	11191
5	4915	11191

prune388.0ms (11.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	429	0	429
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	429	2	431

Error

Counts

431 → 2

Alt Table

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

Status

Error

Program

✓

0.0b

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

✓

0.0b

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

Compiler

Compiled 13885 to 10674 computations (23.1% saved)

regimes99.0ms (3%)

Accuracy

Total 0.0b remaining (31.2%)

Threshold costs 0.0b (31.2%)

Counts

26 → 1

Compiler

Compiled 1824 to 1450 computations (20.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	19	26
2	21	26
3	22	26
4	22	26

end60.0ms (1.8%)

Compiler: Compiled 74 to 58 computations (21.6% saved)

Details

analyze7.0ms (0.2%)

sample1.2s (36.6%)

simplify120.0ms (3.7%)

prune5.0ms (0.2%)

localize10.0ms (0.3%)

series48.0ms (1.4%)

rewrite24.0ms (0.7%)

simplify169.0ms (5.1%)

prune196.0ms (5.9%)

localize18.0ms (0.5%)

series40.0ms (1.2%)

rewrite29.0ms (0.9%)

simplify168.0ms (5.1%)

prune244.0ms (7.4%)

localize11.0ms (0.3%)

series37.0ms (1.1%)

rewrite57.0ms (1.7%)

simplify356.0ms (10.8%)

prune388.0ms (11.8%)

regimes99.0ms (3%)

simplify3.0ms (0.1%)

end60.0ms (1.8%)

Profiling