Details

analyze6.0ms (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 (57.5%)

Results

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

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify24.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1332×	`fma-def_binary64`
553×	`distribute-rgt-in_binary64`
496×	`unsub-neg_binary64`
223×	`distribute-rgt-neg-out_binary64`
221×	`distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	42	28
2	109	26
3	321	26
4	968	26
5	1747	24
6	3706	24

Stop Event

1×	node limit

Counts

1 → 2

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

Compiler

Compiled 113 to 85 computations (24.8% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series50.0ms (2.4%)

Counts

4 → 48

Calls

4 calls:

35.0ms	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
6.0ms	(.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
5.0ms	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
3.0ms	(/.f64 -4/3 (fma.f64 v v -1))

rewrite61.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`
215×	`log-pow_binary64`
142×	`add-sqr-sqrt_binary64`
133×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	294	56
2	3699	56

Stop Event

1×	node limit

Counts

4 → 107

Calls

4 calls:

59.0ms	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
59.0ms	(.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
59.0ms	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
59.0ms	(/.f64 -4/3 (fma.f64 v v -1))

simplify50.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

876×	`times-frac_binary64`
354×	`cancel-sign-sub-inv_binary64`
233×	`fma-neg_binary64`
214×	`sub-neg_binary64`
182×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	1956
1	775	1902
2	2822	1883

Stop Event

1×	node limit

Counts

155 → 189

prune159.0ms (7.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	189	2	191

Error

Counts

191 → 2

Alt Table

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

Compiler

Compiled 5241 to 4015 computations (23.4% saved)

localize11.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series51.0ms (2.5%)

Counts

2 → 24

Calls

2 calls:

35.0ms	(.f64 -4/3 (/.f64 (/.f64 1 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
16.0ms	(/.f64 (/.f64 1 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))

rewrite56.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

267×	`expm1-udef_binary64`
267×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
144×	`add-cbrt-cube_binary64`
144×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	51
1	327	48
2	3953	48

Stop Event

1×	node limit

Counts

2 → 66

Calls

2 calls:

54.0ms	(.f64 -4/3 (/.f64 (/.f64 1 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
54.0ms	(/.f64 (/.f64 1 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))

simplify66.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

807×	`times-frac_binary64`
785×	`fma-def_binary64`
267×	`sub-neg_binary64`
167×	`fma-neg_binary64`
147×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	1973
1	672	1963
2	2667	1926

Stop Event

1×	node limit

Counts

90 → 114

prune176.0ms (8.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	196	2	198

Error

Counts

198 → 2

Alt Table

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

Compiler

Compiled 6259 to 4901 computations (21.7% saved)

regimes80.0ms (3.9%)

Accuracy

Total 0.0b remaining (39.3%)

Threshold costs 0.0b (39.3%)

Counts

18 → 1

Compiler

Compiled 1552 to 1227 computations (20.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	15	24

Stop Event

1×

saturated

end58.0ms (2.8%)

Compiler: Compiled 70 to 54 computations (22.9% saved)

Details

analyze6.0ms (0.3%)

sample1.2s (57.5%)

simplify24.0ms (1.2%)

prune5.0ms (0.2%)

localize11.0ms (0.5%)

series50.0ms (2.4%)

rewrite61.0ms (3%)

simplify50.0ms (2.5%)

prune159.0ms (7.8%)

localize11.0ms (0.6%)

series51.0ms (2.5%)

rewrite56.0ms (2.7%)

simplify66.0ms (3.3%)

prune176.0ms (8.6%)

regimes80.0ms (3.9%)

simplify2.0ms (0.1%)

end58.0ms (2.8%)

Profiling