Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample887.0ms (9.7%)

Results

872.0ms

8256×

body

128

valid

Compiler

Compiled 48 to 32 computations (33.3% saved)

preprocess34.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

794×	`fma-neg_binary64`
524×	`cancel-sign-sub-inv_binary64`
499×	`associate-l_binary64`
406×	`fma-def_binary64`
322×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	40
1	49	40
2	148	40
3	425	40
4	1005	40
5	3108	40
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify36.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-neg_binary64`
595×	`fma-def_binary64`
382×	`distribute-rgt-neg-in_binary64`
265×	`distribute-lft-neg-in_binary64`
256×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	29	20
2	82	20
3	235	20
4	491	20
5	1107	20
6	2177	20
7	3939	20
8	4811	20

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

52.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	52.0b	(fma.f64 y (*.f64 y 2) (neg.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))

Compiler

Compiled 63 to 45 computations (28.6% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	23.0b	(fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))

series13.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))	y	0
2.0ms	(fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))	y	-inf
2.0ms	(fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))	y	inf
2.0ms	(fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))	x	0
2.0ms	(fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))	x	-inf

rewrite34.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

688×	`pow1_binary64`
638×	`add-log-exp_binary64`
638×	`log1p-expm1-u_binary64`
638×	`expm1-log1p-u_binary64`
79×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	169	11
2	1810	11

Stop Event

1×	node limit

Counts

1 → 22

simplify34.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-def_binary64`
408×	`unswap-sqr_binary64`
403×	`cancel-sign-sub-inv_binary64`
313×	`distribute-rgt-neg-in_binary64`
279×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	267
1	23	267
2	51	231
3	125	231
4	350	231
5	1194	231
6	2199	231
7	3710	231

Stop Event

1×	node limit

Counts

46 → 27

prune18.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	1	28

Error

52.0b

Counts

28 → 1

Alt Table

Status	Error	Program
▶	52.0b	(fma.f64 y (*.f64 y 2) (neg.f64 (exp.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))))

Compiler

Compiled 534 to 407 computations (23.8% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.0b	(exp.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))
	23.0b	(fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))

series13.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(exp.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))	y	0
2.0ms	(exp.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))	y	inf
2.0ms	(exp.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))	y	-inf
2.0ms	(exp.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))	x	0
2.0ms	(exp.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))	x	-inf

rewrite45.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

757×	`pow1_binary64`
700×	`log1p-expm1-u_binary64`
700×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`
87×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	193	11
2	1996	11

Stop Event

1×	node limit

Counts

1 → 25

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-def_binary64`
408×	`unswap-sqr_binary64`
403×	`cancel-sign-sub-inv_binary64`
313×	`distribute-rgt-neg-in_binary64`
279×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	267
1	23	267
2	51	231
3	125	231
4	350	231
5	1194	231
6	2199	231
7	3710	231

Stop Event

1×	node limit

Counts

49 → 29

prune33.0ms (0.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	1	57

Error

52.0b

Counts

57 → 1

Alt Table

Status	Error	Program
▶	52.0b	(fma.f64 y (*.f64 y 2) (neg.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))))

Compiler

Compiled 1168 to 906 computations (22.4% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.6b	(exp.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))
✓	3.5b	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))
	23.0b	(fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))

series1.6s (17.6%)

Counts

2 → 48

Calls

12 calls:

347.0ms	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))	y	0
277.0ms	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))	x	0
260.0ms	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))	x	inf
204.0ms	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))	x	-inf
199.0ms	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))))) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))	y	inf

rewrite45.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

861×	`log1p-expm1-u_binary64`
861×	`expm1-log1p-u_binary64`
107×	`add-sqr-sqrt_binary64`
105×	`add-log-exp_binary64`
105×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	246	28
2	2492	28

Stop Event

1×	node limit

Counts

2 → 41

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

335×	`times-frac_binary64`
307×	`associate-/l*_binary64`
291×	`associate-/r*_binary64`
291×	`fma-def_binary64`
268×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	385	4881
1	1345	4380

Stop Event

1×	node limit

Counts

89 → 107

prune214.0ms (2.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	1	162

Error

52.0b

Counts

162 → 1

Alt Table

Status	Error	Program
▶	52.0b	(fma.f64 y (*.f64 y 2) (neg.f64 (pow.f64 (pow.f64 (exp.f64 (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))))

Status

Error

Program

▶

52.0b

(fma.f64 y (*.f64 y 2) (neg.f64 (pow.f64 (pow.f64 (exp.f64 (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))))

Compiler

Compiled 9416 to 7805 computations (17.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(exp.f64 (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4))
✓	1.6b	(pow.f64 (exp.f64 (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4))
✓	3.5b	(pow.f64 (pow.f64 (exp.f64 (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))
	23.0b	(fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))

series4.8s (52.5%)

Counts

3 → 72

Calls

18 calls:

886.0ms	(pow.f64 (pow.f64 (exp.f64 (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))	y	0
787.0ms	(pow.f64 (pow.f64 (exp.f64 (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))	x	inf
749.0ms	(pow.f64 (pow.f64 (exp.f64 (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))	x	-inf
669.0ms	(pow.f64 (pow.f64 (exp.f64 (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))	x	0
292.0ms	(pow.f64 (pow.f64 (exp.f64 (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (pow.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4))) 1/4)) (sqrt.f64 (log.f64 (fma.f64 (pow.f64 x 4) -9 (pow.f64 y 4)))))	y	-inf

rewrite56.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

556×	`log-prod_binary64`
227×	`log-pow_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
146×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	107
1	317	46
2	3492	46

Stop Event

1×	node limit

Counts

3 → 86

simplify157.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

609×	`*-commutative_binary64`
295×	`+-commutative_binary64`
276×	`fma-def_binary64`
238×	`associate-+r+_binary64`
235×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1394	19131

Stop Event

1×	node limit

Counts

158 → 207

prune780.0ms (8.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	287	1	288
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	288	1	289

Error

Counts

289 → 1

Alt Table

Status	Error	Program
	0b	(fma.f64 y (.f64 y 2) (neg.f64 (fma.f64 (.f64 y y) (.f64 y y) (.f64 (pow.f64 x 4) -9))))

Compiler

Compiled 34475 to 28496 computations (17.3% saved)

regimes115.0ms (1.3%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

13 → 1

Compiler

Compiled 3315 to 2637 computations (20.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-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	13	26
1	19	26
2	21	26
3	22	26

Stop Event

1×

saturated

end44.0ms (0.5%)

Stop Event

1×

fuel

Compiler

Compiled 60 to 36 computations (40% saved)

Details

analyze1.0ms (0%)

sample887.0ms (9.7%)

preprocess34.0ms (0.4%)

simplify36.0ms (0.4%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

series13.0ms (0.1%)

rewrite34.0ms (0.4%)

simplify34.0ms (0.4%)

prune18.0ms (0.2%)

localize12.0ms (0.1%)

series13.0ms (0.1%)

rewrite45.0ms (0.5%)

simplify37.0ms (0.4%)

prune33.0ms (0.4%)

localize17.0ms (0.2%)

series1.6s (17.6%)

rewrite45.0ms (0.5%)

simplify70.0ms (0.8%)

prune214.0ms (2.3%)

localize21.0ms (0.2%)

series4.8s (52.5%)

rewrite56.0ms (0.6%)

simplify157.0ms (1.7%)

prune780.0ms (8.5%)

regimes115.0ms (1.3%)

simplify2.0ms (0%)

end44.0ms (0.5%)

Profiling