Details

analyze2.3s (19.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

Compiler

Compiled 28 to 19 computations (32.1% saved)

sample2.7s (22.7%)

Results

1.4s	8256×	body	128	valid
1.3s	7314×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

preprocess46.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

647×	`fma-def_binary64`
618×	`distribute-lft-in_binary64`
618×	`distribute-rgt-in_binary64`
548×	`cancel-sign-sub-inv_binary64`
330×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	188	754
1	558	696
2	1885	696
0	8	8
1	8	8

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort x y)

(sort z t)

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-def_binary64`
441×	`fma-neg_binary64`
435×	`distribute-rgt-in_binary64`
372×	`distribute-lft-in_binary64`
298×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	37	24
2	104	24
3	371	24
4	1368	24
5	3595	24

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0%)

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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.8b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 (.f64 (+.f64 a (.f64 b c)) c) i)))
▶	1.5b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))

Compiler

Compiled 148 to 93 computations (37.2% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (.f64 x y)))
✓	1.8b	(fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (.f64 x y))

series87.0ms (0.7%)

Counts

2 → 168

Calls

42 calls:

3.0ms	(fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (.f64 x y))	x	0
3.0ms	(fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (.f64 x y)))	t	0
3.0ms	(fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (.f64 x y)))	x	inf
3.0ms	(fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (.f64 x y))	b	-inf
2.0ms	(fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (.f64 x y)))	c	-inf

rewrite58.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

334×	`prod-diff_binary64`
263×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
142×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	38
1	300	34
2	3731	34

Stop Event

1×	node limit

Counts

2 → 47

simplify109.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

924×	`fma-neg_binary64`
631×	`cancel-sign-sub-inv_binary64`
426×	`fma-def_binary64`
246×	`distribute-rgt-neg-in_binary64`
241×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	3618
1	158	3216
2	355	3082
3	858	2814
4	2495	2814
5	4929	2814

Stop Event

1×	node limit

Counts

215 → 80

prune73.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Error

0.0b

Counts

82 → 6

Alt Table

Status	Error	Program
	29.2b	(.f64 2 (fma.f64 z t (.f64 -1 (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i))))
✓	1.5b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))
	28.3b	(.f64 2 (fma.f64 z t (.f64 c (*.f64 (neg.f64 i) (fma.f64 c b a)))))
▶	4.8b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (.f64 i (.f64 c (fma.f64 c b a))))))
	16.7b	(.f64 2 (-.f64 (fma.f64 y x (.f64 t z)) (.f64 c (.f64 c (*.f64 i b)))))
	49.4b	(.f64 2 (neg.f64 (+.f64 (.f64 c (.f64 a i)) (.f64 (pow.f64 c 2) (*.f64 i b)))))

Compiler

Compiled 1878 to 656 computations (65.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y x (-.f64 (.f64 t z) (.f64 i (*.f64 c (fma.f64 c b a)))))
✓	0.0b	(-.f64 (.f64 t z) (.f64 i (*.f64 c (fma.f64 c b a))))
✓	0.1b	(*.f64 c (fma.f64 c b a))
✓	7.5b	(.f64 i (.f64 c (fma.f64 c b a)))

series122.0ms (1%)

Counts

4 → 252

Calls

63 calls:

6.0ms	(-.f64 (.f64 t z) (.f64 i (*.f64 c (fma.f64 c b a))))	i	inf
5.0ms	(fma.f64 y x (-.f64 (.f64 t z) (.f64 i (*.f64 c (fma.f64 c b a)))))	y	0
4.0ms	(fma.f64 y x (-.f64 (.f64 t z) (.f64 i (*.f64 c (fma.f64 c b a)))))	z	-inf
4.0ms	(.f64 i (.f64 c (fma.f64 c b a)))	b	-inf
2.0ms	(fma.f64 y x (-.f64 (.f64 t z) (.f64 i (*.f64 c (fma.f64 c b a)))))	b	-inf

rewrite76.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

298×	`expm1-udef_binary64`
298×	`log1p-udef_binary64`
165×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	57
1	319	57
2	4208	57

Stop Event

1×	node limit

Counts

4 → 109

simplify114.0ms (1%)

Algorithm

1×	egg-herbie

Rules

928×	`fma-neg_binary64`
705×	`cancel-sign-sub-inv_binary64`
487×	`fma-def_binary64`
265×	`associate-l_binary64`
258×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	4590
1	163	3669
2	382	3588
3	947	3588
4	2710	3588

Stop Event

1×	node limit

Counts

361 → 159

prune168.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	155	4	159
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	157	8	165

Error

0.0b

Counts

165 → 8

Alt Table

Status	Error	Program
▶	5.8b	(.f64 2 (fma.f64 y x (+.f64 (-.f64 (.f64 t z) (.f64 (fma.f64 c b a) (.f64 i c))) (+.f64 (fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (.f64 i c))) (fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (.f64 i c)))))))
	11.9b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (.f64 c (.f64 i a)))))
	20.9b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (.f64 i (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3))))))
✓	4.8b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (.f64 i (.f64 c (fma.f64 c b a))))))
	16.7b	(.f64 2 (-.f64 (fma.f64 y x (.f64 t z)) (.f64 c (.f64 c (*.f64 i b)))))
	49.4b	(.f64 2 (neg.f64 (+.f64 (.f64 c (.f64 a i)) (.f64 (pow.f64 c 2) (*.f64 i b)))))
	24.4b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (pow.f64 (sqrt.f64 (.f64 (fma.f64 c b a) (.f64 i c))) 2))))
✓	1.5b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))

Compiler

Compiled 4285 to 1285 computations (70% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 t z) (.f64 (fma.f64 c b a) (*.f64 i c)))
✓	0.1b	(*.f64 (fma.f64 c b a) (neg.f64 c))
✓	4.5b	(.f64 (fma.f64 c b a) (.f64 i c))
✓	47.6b	(fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (*.f64 i c)))

series123.0ms (1%)

Counts

4 → 204

Calls

51 calls:

7.0ms	(fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (*.f64 i c)))	a	inf
6.0ms	(fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (*.f64 i c)))	b	0
6.0ms	(fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (*.f64 i c)))	a	-inf
5.0ms	(fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (*.f64 i c)))	b	inf
5.0ms	(fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (*.f64 i c)))	i	-inf

rewrite67.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

272×	`log1p-udef_binary64`
168×	`add-sqr-sqrt_binary64`
164×	`associate-r_binary64`
156×	`log1p-expm1-u_binary64`
156×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	62
1	326	56
2	4555	56

Stop Event

1×	node limit

Counts

4 → 108

simplify92.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

929×	`fma-neg_binary64`
313×	`fma-def_binary64`
292×	`associate-l_binary64`
253×	`unsub-neg_binary64`
242×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	2628
1	173	2052
2	409	1971
3	915	1971
4	2616	1971
5	4750	1971

Stop Event

1×	node limit

Counts

312 → 147

prune332.0ms (2.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	257	9	266

Error

Counts

266 → 9

Alt Table

Status	Error	Program
✓	5.8b	(.f64 2 (fma.f64 y x (+.f64 (-.f64 (.f64 t z) (.f64 (fma.f64 c b a) (.f64 i c))) (+.f64 (fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (.f64 i c))) (fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (.f64 i c)))))))
	11.9b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (.f64 c (.f64 i a)))))
▶	9.3b	(.f64 2 (fma.f64 y x (+.f64 (-.f64 (.f64 t z) (.f64 (fma.f64 c b a) (.f64 i c))) (+.f64 (fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (.f64 i c))) (fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (pow.f64 (cbrt.f64 (.f64 c (.f64 (fma.f64 c b a) i))) 3))))))
	20.9b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (.f64 i (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3))))))
✓	4.8b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (.f64 i (.f64 c (fma.f64 c b a))))))
	16.7b	(.f64 2 (-.f64 (fma.f64 y x (.f64 t z)) (.f64 c (.f64 c (*.f64 i b)))))
	49.4b	(.f64 2 (neg.f64 (+.f64 (.f64 c (.f64 a i)) (.f64 (pow.f64 c 2) (*.f64 i b)))))
	24.4b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (pow.f64 (sqrt.f64 (.f64 (fma.f64 c b a) (.f64 i c))) 2))))
✓	1.5b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))

Compiler

Compiled 15387 to 2321 computations (84.9% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.5b	(.f64 (fma.f64 c b a) (.f64 i c))
✓	13.3b	(cbrt.f64 (.f64 c (.f64 (fma.f64 c b a) i)))
✓	47.0b	(fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (pow.f64 (cbrt.f64 (.f64 c (*.f64 (fma.f64 c b a) i))) 3))
	47.6b	(fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (*.f64 i c)))

series3.7s (30.7%)

Counts

2 → 96

Calls

24 calls:

2.3s	(fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (pow.f64 (cbrt.f64 (.f64 c (*.f64 (fma.f64 c b a) i))) 3))	a	0
664.0ms	(fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (pow.f64 (cbrt.f64 (.f64 c (*.f64 (fma.f64 c b a) i))) 3))	b	0
145.0ms	(cbrt.f64 (.f64 c (.f64 (fma.f64 c b a) i)))	i	0
91.0ms	(cbrt.f64 (.f64 c (.f64 (fma.f64 c b a) i)))	i	-inf
85.0ms	(cbrt.f64 (.f64 c (.f64 (fma.f64 c b a) i)))	i	inf

rewrite60.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`log-prod_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
199×	`log-pow_binary64`
149×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	288	34
2	3474	32

Stop Event

1×	node limit

Counts

2 → 61

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

280×	`times-frac_binary64`
276×	`fma-neg_binary64`
263×	`associate-r_binary64`
238×	`associate-/l*_binary64`
201×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	346	5166
1	1240	4396
2	4727	4265

Stop Event

1×	node limit

Counts

157 → 180

prune376.0ms (3.2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	265	9	274

Error

Counts

274 → 9

Alt Table

Status	Error	Program
✓	5.8b	(.f64 2 (fma.f64 y x (+.f64 (-.f64 (.f64 t z) (.f64 (fma.f64 c b a) (.f64 i c))) (+.f64 (fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (.f64 i c))) (fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (.f64 i c)))))))
	11.9b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (.f64 c (.f64 i a)))))
✓	9.3b	(.f64 2 (fma.f64 y x (+.f64 (-.f64 (.f64 t z) (.f64 (fma.f64 c b a) (.f64 i c))) (+.f64 (fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (.f64 (fma.f64 c b a) (.f64 i c))) (fma.f64 (.f64 (fma.f64 c b a) (neg.f64 c)) i (pow.f64 (cbrt.f64 (.f64 c (.f64 (fma.f64 c b a) i))) 3))))))
	20.9b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (.f64 i (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3))))))
✓	4.8b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (.f64 i (.f64 c (fma.f64 c b a))))))
	16.7b	(.f64 2 (-.f64 (fma.f64 y x (.f64 t z)) (.f64 c (.f64 c (*.f64 i b)))))
	49.4b	(.f64 2 (neg.f64 (+.f64 (.f64 c (.f64 a i)) (.f64 (pow.f64 c 2) (*.f64 i b)))))
	24.4b	(.f64 2 (fma.f64 y x (-.f64 (.f64 t z) (pow.f64 (sqrt.f64 (.f64 (fma.f64 c b a) (.f64 i c))) 2))))
✓	1.5b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))

Compiler

Compiled 18704 to 5043 computations (73% saved)

regimes987.0ms (8.3%)

Accuracy

Total 2.0b remaining (99.2%)

Threshold costs 0b (0%)

Counts

57 → 1

Compiler

Compiled 27693 to 16259 computations (41.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	26	24
2	34	24
3	40	24
4	43	24
5	44	24

Stop Event

1×

saturated

end160.0ms (1.3%)

Stop Event

1×

fuel

Remove

(sort z t)

(sort x y)

Compiler

Compiled 451 to 263 computations (41.7% saved)

Details

analyze2.3s (19.3%)

sample2.7s (22.7%)

preprocess46.0ms (0.4%)

simplify26.0ms (0.2%)

prune5.0ms (0%)

localize13.0ms (0.1%)

series87.0ms (0.7%)

rewrite58.0ms (0.5%)

simplify109.0ms (0.9%)

prune73.0ms (0.6%)

localize13.0ms (0.1%)

series122.0ms (1%)

rewrite76.0ms (0.6%)

simplify114.0ms (1%)

prune168.0ms (1.4%)

localize20.0ms (0.2%)

series123.0ms (1%)

rewrite67.0ms (0.6%)

simplify92.0ms (0.8%)

prune332.0ms (2.8%)

localize27.0ms (0.2%)

series3.7s (30.7%)

rewrite60.0ms (0.5%)

simplify96.0ms (0.8%)

prune376.0ms (3.2%)

regimes987.0ms (8.3%)

simplify3.0ms (0%)

end160.0ms (1.3%)

Profiling