Details

analyze34.0ms (1.1%)

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
48.4%	1.6%	50%	9
48.4%	1.6%	50%	10
48.4%	1.6%	50%	11
48.5%	1.5%	50%	12
48.6%	1.4%	50.1%	13
48.6%	1.3%	50.1%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.1s (36.8%)

Results

1.0s	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify47.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1030×	`fma-def_binary64`
455×	`distribute-lft-in_binary64`
455×	`distribute-rgt-in_binary64`
427×	`unsub-neg_binary64`
285×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	42	28
2	119	26
3	368	26
4	1099	26
5	2659	26

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

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 (neg.f64 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 (neg.f64 v) 1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

Compiler

Compiled 116 to 88 computations (24.1% saved)

localize15.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1))
✓	1.0b	(/.f64 4/3 (*.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)))

series11.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(/.f64 4/3 (*.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)))
4.0ms	(*.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

3.0ms	(/.f64 4/3 (*.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)))
3.0ms	(*.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1))

simplify514.0ms (17.3%)

Algorithm

1×	egg-herbie

Rules

451×	`associate-r_binary64`
451×	`associate-l_binary64`
388×	`associate-/r*_binary64`
333×	`fma-neg_binary64`
258×	`fma-def_binary64`

Counts

69 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1288
1	308	1132
2	1124	1124
3	4850	1122

prune83.0ms (2.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	1	95

Error

Counts

95 → 1

Alt Table

Status	Error	Program
▶	0b	(/.f64 (/.f64 4/3 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64)))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Compiler

Compiled 2205 to 1481 computations (32.8% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (PI.f64) (*.f64 (pow.f64 v 2) (PI.f64)))
✓	0.2b	(*.f64 (pow.f64 v 2) (PI.f64))
✓	1.0b	(/.f64 4/3 (-.f64 (PI.f64) (*.f64 (pow.f64 v 2) (PI.f64))))

series14.0ms (0.5%)

Counts

3 → 15

Calls

3 calls:

6.0ms	(/.f64 4/3 (-.f64 (PI.f64) (*.f64 (pow.f64 v 2) (PI.f64))))
4.0ms	(-.f64 (PI.f64) (*.f64 (pow.f64 v 2) (PI.f64)))
3.0ms	(*.f64 (pow.f64 v 2) (PI.f64))

rewrite24.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 85

Calls

3 calls:

4.0ms	(*.f64 (pow.f64 v 2) (PI.f64))
3.0ms	(/.f64 4/3 (-.f64 (PI.f64) (*.f64 (pow.f64 v 2) (PI.f64))))
2.0ms	(-.f64 (PI.f64) (*.f64 (pow.f64 v 2) (PI.f64)))

simplify884.0ms (29.8%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-neg_binary64`
406×	`associate-/r*_binary64`
389×	`fma-def_binary64`
387×	`times-frac_binary64`
294×	`*-commutative_binary64`

Counts

100 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2018
1	434	1731
2	1299	1687
3	4988	1687

prune123.0ms (4.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	162	1	163

Error

Counts

163 → 1

Alt Table

Status	Error	Program
✓	0b	(/.f64 (/.f64 4/3 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64)))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Compiler

Compiled 4006 to 2746 computations (31.5% saved)

regimes27.0ms (0.9%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

5 → 1

Compiler

Compiled 436 to 334 computations (23.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
4×	`cancel-sign-sub-inv_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	21	27
2	34	27
3	40	27
4	44	27
5	45	27

soundness22.0ms (0.7%)

Compiler: Compiled 739 to 562 computations (24% saved)

end47.0ms (1.6%)

Compiler: Compiled 54 to 42 computations (22.2% saved)

Details

analyze34.0ms (1.1%)

sample1.1s (36.8%)

simplify47.0ms (1.6%)

prune5.0ms (0.2%)

localize15.0ms (0.5%)

series11.0ms (0.4%)

rewrite8.0ms (0.3%)

simplify514.0ms (17.3%)

prune83.0ms (2.8%)

localize13.0ms (0.4%)

series14.0ms (0.5%)

rewrite24.0ms (0.8%)

simplify884.0ms (29.8%)

prune123.0ms (4.2%)

regimes27.0ms (0.9%)

simplify4.0ms (0.1%)

soundness22.0ms (0.7%)

end47.0ms (1.6%)

Profiling