Details

analyze2.4s (28%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
1.1%	98.6%	0.3%	12
1.9%	97.8%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.7s (19%)

Results

1.6s	8254×	body	128	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 83 to 50 computations (39.8% saved)

simplify34.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-neg_binary64`
497×	`fma-def_binary64`
495×	`cancel-sign-sub-inv_binary64`
376×	`sub-neg_binary64`
334×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	37	29
2	89	29
3	253	27
4	623	27
5	1451	27
6	2919	27

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

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

24.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.9b	(/.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))) (+.f64 x (+.f64 y t)))

Compiler

Compiled 96 to 52 computations (45.8% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.0b	(fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z)))
✓	1.3b	(fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))
✓	23.3b	(/.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))) (+.f64 x (+.f64 y t)))

series197.0ms (2.3%)

Counts

3 → 204

Calls

3 calls:

142.0ms	(/.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))) (+.f64 x (+.f64 y t)))
34.0ms	(fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z)))
20.0ms	(fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))

rewrite41.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

184×	`add-sqr-sqrt_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`
177×	`add-cbrt-cube_binary64`
170×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	348	59

Stop Event

1×	node limit

Counts

3 → 76

Calls

3 calls:

39.0ms	(fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z)))
39.0ms	(fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))
39.0ms	(/.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))) (+.f64 x (+.f64 y t)))

simplify131.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

834×	`times-frac_binary64`
564×	`associate-/l*_binary64`
364×	`associate-/r*_binary64`
256×	`+-commutative_binary64`
210×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	568	9417
1	1942	9294

Stop Event

1×	node limit

Counts

280 → 185

prune203.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	178	7	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	178	8	186

Error

0.0b

Counts

186 → 8

Alt Table

Status	Error	Program
	24.9b	(pow.f64 (/.f64 (+.f64 (+.f64 x y) t) (fma.f64 t a (fma.f64 y (-.f64 (+.f64 a z) b) (*.f64 z x)))) -1)
	37.7b	(/.f64 a (/.f64 (+.f64 y (+.f64 x t)) (+.f64 y t)))
	40.7b	(+.f64 a (-.f64 (+.f64 (.f64 (/.f64 z t) x) (.f64 (/.f64 y t) z)) (+.f64 (.f64 (/.f64 a t) x) (.f64 (/.f64 y t) b))))
	25.0b	(.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 a z) b) (.f64 z x))) (/.f64 1 (+.f64 (+.f64 x y) t)))
	41.7b	(+.f64 (*.f64 (/.f64 t y) b) (-.f64 (+.f64 (+.f64 z a) (/.f64 x (/.f64 y b))) (+.f64 (/.f64 a (/.f64 y x)) (+.f64 b (/.f64 z (/.f64 y t))))))
	39.9b	(+.f64 (.f64 (/.f64 a x) y) (-.f64 (+.f64 z (/.f64 a (/.f64 x t))) (+.f64 (.f64 (/.f64 y x) b) (*.f64 (/.f64 t x) z))))
✓	24.9b	(/.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))) (+.f64 x (+.f64 y t)))
▶	3.7b	(+.f64 (/.f64 y (/.f64 (+.f64 y (+.f64 x t)) z)) (-.f64 (+.f64 (.f64 (/.f64 z (+.f64 y (+.f64 x t))) x) (+.f64 (/.f64 a (/.f64 (+.f64 y (+.f64 x t)) t)) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) a))) (*.f64 (/.f64 y (+.f64 y (+.f64 x t))) b)))

Compiler

Compiled 9219 to 3064 computations (66.8% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.7b	(/.f64 a (/.f64 (+.f64 y (+.f64 x t)) t))
✓	5.5b	(*.f64 (/.f64 y (+.f64 y (+.f64 x t))) a)
✓	7.7b	(/.f64 y (/.f64 (+.f64 y (+.f64 x t)) z))
✓	7.9b	(*.f64 (/.f64 z (+.f64 y (+.f64 x t))) x)

series233.0ms (2.7%)

Counts

4 → 192

Calls

4 calls:

78.0ms	(/.f64 a (/.f64 (+.f64 y (+.f64 x t)) t))
57.0ms	(*.f64 (/.f64 z (+.f64 y (+.f64 x t))) x)
51.0ms	(*.f64 (/.f64 y (+.f64 y (+.f64 x t))) a)
46.0ms	(/.f64 y (/.f64 (+.f64 y (+.f64 x t)) z))

rewrite44.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

192×	`add-sqr-sqrt_binary64`
181×	`log1p-expm1-u_binary64`
181×	`expm1-log1p-u_binary64`
180×	`add-cbrt-cube_binary64`
177×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
1	372	52

Stop Event

1×	node limit

Counts

4 → 104

Calls

4 calls:

42.0ms	(/.f64 a (/.f64 (+.f64 y (+.f64 x t)) t))
42.0ms	(*.f64 (/.f64 y (+.f64 y (+.f64 x t))) a)
42.0ms	(/.f64 y (/.f64 (+.f64 y (+.f64 x t)) z))
42.0ms	(*.f64 (/.f64 z (+.f64 y (+.f64 x t))) x)

simplify122.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

650×	`associate-/l*_binary64`
414×	`associate-/r*_binary64`
302×	`associate-r_binary64`
217×	`sub-neg_binary64`
203×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	588	8996
1	2104	8948

Stop Event

1×	node limit

Counts

296 → 307

prune423.0ms (4.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	304	3	307
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	307	8	315

Error

0.0b

Counts

315 → 8

Alt Table

Status	Error	Program
	24.9b	(pow.f64 (/.f64 (+.f64 (+.f64 x y) t) (fma.f64 t a (fma.f64 y (-.f64 (+.f64 a z) b) (*.f64 z x)))) -1)
	37.7b	(/.f64 a (/.f64 (+.f64 y (+.f64 x t)) (+.f64 y t)))
	14.3b	(+.f64 (.f64 (/.f64 y (+.f64 x t)) z) (-.f64 (+.f64 (.f64 (/.f64 z (+.f64 y (+.f64 x t))) x) (+.f64 (/.f64 a (/.f64 (+.f64 y (+.f64 x t)) t)) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) a))) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) b)))
✓	24.9b	(/.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))) (+.f64 x (+.f64 y t)))
▶	4.9b	(+.f64 (/.f64 y (/.f64 (+.f64 y (+.f64 x t)) z)) (-.f64 (+.f64 (.f64 (/.f64 z (+.f64 y (+.f64 x t))) x) (+.f64 (.f64 (/.f64 a (+.f64 y (+.f64 x t))) t) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) a))) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) b)))
	25.0b	(.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 a z) b) (.f64 z x))) (/.f64 1 (+.f64 (+.f64 x y) t)))
	41.7b	(+.f64 (*.f64 (/.f64 t y) b) (-.f64 (+.f64 (+.f64 z a) (/.f64 x (/.f64 y b))) (+.f64 (/.f64 a (/.f64 y x)) (+.f64 b (/.f64 z (/.f64 y t))))))
	14.3b	(+.f64 (/.f64 y (/.f64 (+.f64 y (+.f64 x t)) z)) (-.f64 (+.f64 z (+.f64 (/.f64 a (/.f64 (+.f64 y (+.f64 x t)) t)) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) a))) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) b)))

Compiler

Compiled 22047 to 4991 computations (77.4% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.5b	(*.f64 (/.f64 y (+.f64 y (+.f64 x t))) a)
✓	7.5b	(*.f64 (/.f64 a (+.f64 y (+.f64 x t))) t)
	7.7b	(/.f64 y (/.f64 (+.f64 y (+.f64 x t)) z))
	7.9b	(*.f64 (/.f64 z (+.f64 y (+.f64 x t))) x)

series46.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

45.0ms

(*.f64 (/.f64 a (+.f64 y (+.f64 x t))) t)

rewrite61.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

384×	`fma-def_binary64`
207×	`fma-neg_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
173×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	207	13
2	3169	13

Stop Event

1×	node limit

Counts

1 → 25

Calls

1 calls:

61.0ms

(*.f64 (/.f64 a (+.f64 y (+.f64 x t))) t)

simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

358×	`times-frac_binary64`
328×	`cancel-sign-sub-inv_binary64`
254×	`fma-neg_binary64`
220×	`associate-/l*_binary64`
176×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	2250
1	776	2238
2	2904	1947

Stop Event

1×	node limit

Counts

73 → 78

prune517.0ms (6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	301	1	302
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	303	7	310

Error

0.0b

Counts

310 → 7

Alt Table

Status	Error	Program
	24.9b	(pow.f64 (/.f64 (+.f64 (+.f64 x y) t) (fma.f64 t a (fma.f64 y (-.f64 (+.f64 a z) b) (*.f64 z x)))) -1)
	37.7b	(/.f64 a (/.f64 (+.f64 y (+.f64 x t)) (+.f64 y t)))
	25.0b	(.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 a z) b) (.f64 z x))) (/.f64 1 (+.f64 (+.f64 x y) t)))
	41.7b	(+.f64 (*.f64 (/.f64 t y) b) (-.f64 (+.f64 (+.f64 z a) (/.f64 x (/.f64 y b))) (+.f64 (/.f64 a (/.f64 y x)) (+.f64 b (/.f64 z (/.f64 y t))))))
▶	10.3b	(+.f64 (.f64 (/.f64 y (+.f64 y t)) z) (-.f64 (+.f64 (.f64 (/.f64 z (+.f64 y (+.f64 x t))) x) (+.f64 (.f64 (/.f64 a (+.f64 y (+.f64 x t))) t) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) a))) (*.f64 (/.f64 y (+.f64 y (+.f64 x t))) b)))
✓	24.9b	(/.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))) (+.f64 x (+.f64 y t)))
	14.3b	(+.f64 (/.f64 y (/.f64 (+.f64 y (+.f64 x t)) z)) (-.f64 (+.f64 z (+.f64 (/.f64 a (/.f64 (+.f64 y (+.f64 x t)) t)) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) a))) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) b)))

Compiler

Compiled 21456 to 4855 computations (77.4% saved)

localize43.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.2b	(*.f64 (/.f64 y (+.f64 y t)) z)
	5.5b	(*.f64 (/.f64 y (+.f64 y (+.f64 x t))) a)
	7.5b	(*.f64 (/.f64 a (+.f64 y (+.f64 x t))) t)
	7.9b	(*.f64 (/.f64 z (+.f64 y (+.f64 x t))) x)

series20.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

20.0ms

(*.f64 (/.f64 y (+.f64 y t)) z)

rewrite49.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

876×	`log1p-expm1-u_binary64`
876×	`expm1-log1p-u_binary64`
473×	`prod-diff_binary64`
82×	`add-sqr-sqrt_binary64`
77×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	156	10
2	2298	10

Stop Event

1×	node limit

Counts

1 → 25

Calls

1 calls:

48.0ms

(*.f64 (/.f64 y (+.f64 y t)) z)

simplify35.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

638×	`cancel-sign-sub-inv_binary64`
526×	`fma-def_binary64`
362×	`associate-/r/_binary64`
349×	`fma-neg_binary64`
330×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	702
1	109	702
2	326	636
3	1614	561

Stop Event

1×	node limit

Counts

61 → 41

prune339.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	262	6	268

Error

0.0b

Counts

268 → 6

Alt Table

Status	Error	Program
	22.0b	(+.f64 (.f64 (/.f64 y (+.f64 y t)) z) (-.f64 (+.f64 (.f64 (/.f64 z (+.f64 y (+.f64 x t))) x) (+.f64 (.f64 (/.f64 a (+.f64 y (+.f64 x t))) t) (/.f64 a (/.f64 (+.f64 x t) y)))) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) b)))
	41.7b	(+.f64 (*.f64 (/.f64 t y) b) (-.f64 (+.f64 (+.f64 z a) (/.f64 x (/.f64 y b))) (+.f64 (/.f64 a (/.f64 y x)) (+.f64 b (/.f64 z (/.f64 y t))))))
	25.0b	(.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 a z) b) (.f64 z x))) (/.f64 1 (+.f64 (+.f64 x y) t)))
	24.9b	(pow.f64 (/.f64 (+.f64 (+.f64 x y) t) (fma.f64 t a (fma.f64 y (-.f64 (+.f64 a z) b) (*.f64 z x)))) -1)
✓	24.9b	(/.f64 (fma.f64 t a (fma.f64 y (-.f64 (+.f64 z a) b) (*.f64 x z))) (+.f64 x (+.f64 y t)))
	14.3b	(+.f64 (/.f64 y (/.f64 (+.f64 y (+.f64 x t)) z)) (-.f64 (+.f64 z (+.f64 (/.f64 a (/.f64 (+.f64 y (+.f64 x t)) t)) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) a))) (.f64 (/.f64 y (+.f64 y (+.f64 x t))) b)))

Compiler

Compiled 17389 to 4021 computations (76.9% saved)

regimes1.8s (20.7%)

Accuracy

Total 0.8b remaining (94.5%)

Threshold costs 0.8b (94.5%)

Counts

147 → 3

Compiler

Compiled 41536 to 19452 computations (53.2% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 27 to 16 computations (40.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`+-commutative_binary64`
16×	`*-commutative_binary64`
9×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	291
1	90	291
2	116	291
3	128	291
4	135	291
5	136	291

Stop Event

1×

saturated

end131.0ms (1.5%)

Compiler: Compiled 614 to 204 computations (66.8% saved)

Details

analyze2.4s (28%)

sample1.7s (19%)

simplify34.0ms (0.4%)

prune4.0ms (0%)

localize14.0ms (0.2%)

series197.0ms (2.3%)

rewrite41.0ms (0.5%)

simplify131.0ms (1.5%)

prune203.0ms (2.3%)

localize19.0ms (0.2%)

series233.0ms (2.7%)

rewrite44.0ms (0.5%)

simplify122.0ms (1.4%)

prune423.0ms (4.9%)

localize23.0ms (0.3%)

series46.0ms (0.5%)

rewrite61.0ms (0.7%)

simplify52.0ms (0.6%)

prune517.0ms (6%)

localize43.0ms (0.5%)

series20.0ms (0.2%)

rewrite49.0ms (0.6%)

simplify35.0ms (0.4%)

prune339.0ms (3.9%)

regimes1.8s (20.7%)

bsearch8.0ms (0.1%)

simplify8.0ms (0.1%)

end131.0ms (1.5%)

Profiling