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)

sample967.0ms (46.8%)

Results

954.0ms	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 44 to 34 computations (22.7% saved)

preprocess34.0ms (1.6%)

Algorithm

2×	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: 0 (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
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify24.0ms (1.1%)

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)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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	(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 (fma.f64 v v -1))

series32.0ms (1.6%)

Counts

4 → 48

Calls

12 calls:

7.0ms	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))	v	0
6.0ms	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))	v	-inf
6.0ms	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))	v	inf
2.0ms	(.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))	v	0
2.0ms	(.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))	v	-inf

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

simplify50.0ms (2.4%)

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

prune165.0ms (8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	188	3	191

Error

Counts

191 → 3

Alt Table

Status	Error	Program
	0.0b	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 3)))
▶	0.0b	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 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 5281 to 4033 computations (23.6% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series31.0ms (1.5%)

Counts

3 → 36

Calls

9 calls:

7.0ms	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2))))	v	inf
6.0ms	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2))))	v	0
6.0ms	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2))))	v	-inf
2.0ms	(sqrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2)))	v	0
2.0ms	(.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2))	v	inf

rewrite60.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

261×	`expm1-udef_binary64`
261×	`log1p-udef_binary64`
229×	`log-pow_binary64`
149×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	315	53
2	3824	53

Stop Event

1×	node limit

Counts

3 → 87

simplify53.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
546×	`associate-/l*_binary64`
322×	`cancel-sign-sub-inv_binary64`
176×	`fma-neg_binary64`
166×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	1662
1	626	1583
2	2320	1495

Stop Event

1×	node limit

Counts

123 → 137

prune182.0ms (8.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	174	3	177

Error

Counts

177 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2))))
✓	0.0b	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
▶	0.2b	(/.f64 (fma.f64 4/3 (.f64 v v) 4/3) (sqrt.f64 (.f64 (fma.f64 v (*.f64 v -6) 2) (pow.f64 (PI.f64) 2))))

Compiler

Compiled 4874 to 3735 computations (23.4% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

series14.0ms (0.7%)

Counts

1 → 12

Calls

3 calls:

5.0ms

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

inf

4.0ms

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

-inf

4.0ms

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

rewrite49.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

640×	`log-prod_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
216×	`log-pow_binary64`
137×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	291	24
2	3434	24

Stop Event

1×	node limit

Counts

1 → 39

simplify34.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

564×	`times-frac_binary64`
529×	`associate-/r*_binary64`
321×	`fma-def_binary64`
308×	`associate-/l*_binary64`
288×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	799
1	357	795
2	1341	726

Stop Event

1×	node limit

Counts

51 → 62

prune130.0ms (6.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	134	3	137

Error

Counts

137 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2))))
✓	0.0b	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
✓	0.2b	(/.f64 (fma.f64 4/3 (.f64 v v) 4/3) (sqrt.f64 (.f64 (fma.f64 v (*.f64 v -6) 2) (pow.f64 (PI.f64) 2))))

Compiler

Compiled 3711 to 2670 computations (28.1% saved)

regimes66.0ms (3.2%)

Accuracy

Total 0.0b remaining (31.4%)

Threshold costs 0.0b (31.4%)

Counts

16 → 1

Compiler

Compiled 1271 to 1016 computations (20.1% saved)

simplify2.0ms (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

Stop Event

1×

saturated

end73.0ms (3.5%)

Stop Event

1×

done

Compiler

Compiled 89 to 69 computations (22.5% saved)

Details

analyze6.0ms (0.3%)

sample967.0ms (46.8%)

preprocess34.0ms (1.6%)

simplify24.0ms (1.1%)

prune5.0ms (0.2%)

localize9.0ms (0.5%)

series32.0ms (1.6%)

rewrite61.0ms (3%)

simplify50.0ms (2.4%)

prune165.0ms (8%)

localize10.0ms (0.5%)

series31.0ms (1.5%)

rewrite60.0ms (2.9%)

simplify53.0ms (2.6%)

prune182.0ms (8.8%)

localize10.0ms (0.5%)

series14.0ms (0.7%)

rewrite49.0ms (2.4%)

simplify34.0ms (1.6%)

prune130.0ms (6.3%)

regimes66.0ms (3.2%)

simplify2.0ms (0.1%)

end73.0ms (3.5%)

Profiling