Details

analyze1.2s (19.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.1s (17.9%)

Results

987.0ms	8256×	body	128	valid
78.0ms	691×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify25.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-neg_binary64`
663×	`div-sub_binary64`
241×	`cancel-sign-sub-inv_binary64`
213×	`distribute-neg-frac_binary64`
210×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	53	16
3	100	16
4	210	16
5	422	16
6	913	16
7	2616	16

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

11.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.4b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	11.0b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series54.0ms (0.9%)

Counts

2 → 69

Calls

2 calls:

47.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
6.0ms	(-.f64 x (*.f64 y z))

rewrite65.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

412×	`fma-def_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
195×	`fma-neg_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	253	23
2	3872	23

Stop Event

1×	node limit

Counts

2 → 134

Calls

2 calls:

62.0ms	(-.f64 x (*.f64 y z))
62.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/r*_binary64`
549×	`fma-def_binary64`
458×	`cancel-sign-sub-inv_binary64`
174×	`sub-neg_binary64`
149×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	2839
1	409	2698
2	1881	2491

Stop Event

1×	node limit

Counts

203 → 174

prune143.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	163	11	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	11	175

Error

0.0b

Counts

175 → 11

Alt Table

Status	Error	Program
	11.5b	(pow.f64 (/.f64 (-.f64 t (*.f64 z a)) (fma.f64 y (neg.f64 z) x)) -1)
	39.8b	(/.f64 (neg.f64 (/.f64 (-.f64 x (*.f64 y z)) z)) a)
	36.2b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 t (.f64 z a)))) (/.f64 (fma.f64 y (neg.f64 z) x) (sqrt.f64 (-.f64 t (*.f64 z a)))))
▶	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	12.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)) (/.f64 (fma.f64 y (neg.f64 z) x) (cbrt.f64 (-.f64 t (*.f64 z a)))))
	34.5b	(.f64 (/.f64 y (-.f64 t (.f64 z a))) (neg.f64 z))
	39.0b	(/.f64 y a)
	33.7b	(.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 (.f64 t t) (pow.f64 (*.f64 z a) 2))) (fma.f64 z a t))
	32.7b	(/.f64 (fma.f64 (.f64 (neg.f64 y) (sqrt.f64 z)) (sqrt.f64 z) x) (-.f64 t (.f64 a z)))
	31.2b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 y (neg.f64 z) x) 2)) (.f64 (cbrt.f64 (fma.f64 y (neg.f64 z) x)) (/.f64 1 (-.f64 t (*.f64 z a)))))
	11.9b	(fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (-.f64 t (.f64 z a))) (neg.f64 (/.f64 (.f64 y z) (-.f64 t (*.f64 z a)))))

Compiler

Compiled 4742 to 1540 computations (67.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
✓	3.6b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	12.7b	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))

series129.0ms (2%)

Counts

3 → 114

Calls

3 calls:

66.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
32.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))
30.0ms	(/.f64 x (-.f64 t (*.f64 a z)))

rewrite79.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

270×	`log1p-udef_binary64`
148×	`add-sqr-sqrt_binary64`
144×	`egg-rr`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	279	39
2	4575	39

Stop Event

1×	node limit

Counts

3 → 144

Calls

3 calls:

75.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
75.0ms	(/.f64 x (-.f64 t (*.f64 a z)))
75.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

627×	`associate-/r*_binary64`
618×	`fma-def_binary64`
485×	`cancel-sign-sub-inv_binary64`
199×	`sub-neg_binary64`
169×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	4851
1	463	4575
2	2059	4192

Stop Event

1×	node limit

Counts

258 → 221

prune172.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	215	6	221
Fresh	6	4	10
Picked	0	1	1
Done	0	0	0
Total	221	11	232

Error

Counts

232 → 11

Alt Table

Status	Error	Program
	36.2b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 t (.f64 z a)))) (/.f64 (fma.f64 y (neg.f64 z) x) (sqrt.f64 (-.f64 t (*.f64 z a)))))
✓	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	36.6b	(/.f64 (-.f64 (.f64 x (/.f64 (-.f64 t (.f64 z a)) z)) (.f64 (-.f64 t (.f64 z a)) y)) (.f64 (-.f64 t (.f64 z a)) (/.f64 (-.f64 t (*.f64 z a)) z)))
	12.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)) (/.f64 (fma.f64 y (neg.f64 z) x) (cbrt.f64 (-.f64 t (*.f64 z a)))))
	35.7b	(/.f64 (-.f64 (.f64 (-.f64 t (.f64 z a)) x) (.f64 (.f64 y z) (-.f64 t (.f64 z a)))) (pow.f64 (-.f64 t (.f64 z a)) 2))
	32.9b	(/.f64 (neg.f64 y) (/.f64 (-.f64 t (*.f64 z a)) z))
▶	11.4b	(fma.f64 x (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 (.f64 y (neg.f64 z)) (-.f64 t (*.f64 z a))))
	30.7b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (/.f64 y t) z))
	11.5b	(pow.f64 (/.f64 (-.f64 t (*.f64 z a)) (fma.f64 y (neg.f64 z) x)) -1)
	31.5b	(/.f64 (-.f64 y (/.f64 x z)) a)
	11.9b	(fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (-.f64 t (.f64 z a))) (neg.f64 (/.f64 (.f64 y z) (-.f64 t (*.f64 z a)))))

Compiler

Compiled 6743 to 2031 computations (69.9% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (-.f64 t (*.f64 z a)))
✓	0.9b	(fma.f64 x (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 (.f64 y (neg.f64 z)) (-.f64 t (*.f64 z a))))
✓	12.6b	(/.f64 (.f64 y (neg.f64 z)) (-.f64 t (.f64 z a)))

series116.0ms (1.9%)

Counts

3 → 144

Calls

3 calls:

68.0ms	(fma.f64 x (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 (.f64 y (neg.f64 z)) (-.f64 t (*.f64 z a))))
34.0ms	(/.f64 (.f64 y (neg.f64 z)) (-.f64 t (.f64 z a)))
14.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))

rewrite65.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

925×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
140×	`add-cbrt-cube_binary64`
140×	`log1p-expm1-u_binary64`
140×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	298	42
2	4270	42

Stop Event

1×	node limit

Counts

3 → 97

Calls

3 calls:

63.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))
63.0ms	(fma.f64 x (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 (.f64 y (neg.f64 z)) (-.f64 t (*.f64 z a))))
63.0ms	(/.f64 (.f64 y (neg.f64 z)) (-.f64 t (.f64 z a)))

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
509×	`cancel-sign-sub-inv_binary64`
205×	`sub-neg_binary64`
197×	`associate-/l/_binary64`
183×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	5301
1	533	5065
2	2307	4681

Stop Event

1×	node limit

Counts

241 → 175

prune142.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	175	11	186

Error

Counts

186 → 11

Alt Table

Status	Error	Program
	36.2b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 t (.f64 z a)))) (/.f64 (fma.f64 y (neg.f64 z) x) (sqrt.f64 (-.f64 t (*.f64 z a)))))
✓	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	36.6b	(/.f64 (-.f64 (.f64 x (/.f64 (-.f64 t (.f64 z a)) z)) (.f64 (-.f64 t (.f64 z a)) y)) (.f64 (-.f64 t (.f64 z a)) (/.f64 (-.f64 t (*.f64 z a)) z)))
	12.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)) (/.f64 (fma.f64 y (neg.f64 z) x) (cbrt.f64 (-.f64 t (*.f64 z a)))))
	35.7b	(/.f64 (-.f64 (.f64 (-.f64 t (.f64 z a)) x) (.f64 (.f64 y z) (-.f64 t (.f64 z a)))) (pow.f64 (-.f64 t (.f64 z a)) 2))
	32.9b	(/.f64 (neg.f64 y) (/.f64 (-.f64 t (*.f64 z a)) z))
✓	11.4b	(fma.f64 x (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 (.f64 y (neg.f64 z)) (-.f64 t (*.f64 z a))))
	30.7b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (/.f64 y t) z))
▶	11.5b	(pow.f64 (/.f64 (-.f64 t (*.f64 z a)) (fma.f64 y (neg.f64 z) x)) -1)
	31.5b	(/.f64 (-.f64 y (/.f64 x z)) a)
	11.9b	(fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (-.f64 t (.f64 z a))) (neg.f64 (/.f64 (.f64 y z) (-.f64 t (*.f64 z a)))))

Compiler

Compiled 5431 to 2039 computations (62.5% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (/.f64 (-.f64 t (*.f64 z a)) (fma.f64 y (neg.f64 z) x)) -1)
✓	10.9b	(/.f64 (-.f64 t (*.f64 z a)) (fma.f64 y (neg.f64 z) x))

series195.0ms (3.1%)

Counts

2 → 120

Calls

2 calls:

143.0ms	(pow.f64 (/.f64 (-.f64 t (*.f64 z a)) (fma.f64 y (neg.f64 z) x)) -1)
51.0ms	(/.f64 (-.f64 t (*.f64 z a)) (fma.f64 y (neg.f64 z) x))

rewrite137.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

891×	`prod-diff_binary64`
296×	`egg-rr`
146×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	283	28
2	4009	28

Stop Event

1×	node limit

Counts

2 → 296

Calls

2 calls:

125.0ms	(pow.f64 (/.f64 (-.f64 t (*.f64 z a)) (fma.f64 y (neg.f64 z) x)) -1)
125.0ms	(/.f64 (-.f64 t (*.f64 z a)) (fma.f64 y (neg.f64 z) x))

simplify110.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

654×	`associate-/l*_binary64`
552×	`associate-/r*_binary64`
381×	`associate-l_binary64`
190×	`fma-def_binary64`
141×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	437	10105
1	1682	9761

Stop Event

1×	node limit

Counts

416 → 387

prune336.0ms (5.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	385	2	387
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	388	10	398

Error

Counts

398 → 10

Alt Table

Status	Error	Program
	36.2b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 t (.f64 z a)))) (/.f64 (fma.f64 y (neg.f64 z) x) (sqrt.f64 (-.f64 t (*.f64 z a)))))
✓	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	13.2b	(pow.f64 (-.f64 (/.f64 t (-.f64 x (.f64 z y))) (.f64 (/.f64 a (-.f64 x (*.f64 z y))) z)) -1)
	31.5b	(/.f64 (-.f64 y (/.f64 x z)) a)
	35.7b	(/.f64 (-.f64 (.f64 (-.f64 t (.f64 z a)) x) (.f64 (.f64 y z) (-.f64 t (.f64 z a)))) (pow.f64 (-.f64 t (.f64 z a)) 2))
	32.9b	(/.f64 (neg.f64 y) (/.f64 (-.f64 t (*.f64 z a)) z))
✓	11.4b	(fma.f64 x (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 (.f64 y (neg.f64 z)) (-.f64 t (*.f64 z a))))
	30.7b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (/.f64 y t) z))
	32.7b	(pow.f64 (-.f64 (fma.f64 (/.f64 a (.f64 y y)) (/.f64 x z) (/.f64 a y)) (/.f64 t (.f64 z y))) -1)
	36.6b	(/.f64 (-.f64 (.f64 x (/.f64 (-.f64 t (.f64 z a)) z)) (.f64 (-.f64 t (.f64 z a)) y)) (.f64 (-.f64 t (.f64 z a)) (/.f64 (-.f64 t (*.f64 z a)) z)))

Compiler

Compiled 23956 to 7215 computations (69.9% saved)

regimes1.8s (28.6%)

Accuracy

Total 4.8b remaining (99.7%)

Threshold costs 0b (0%)

Counts

160 → 3

Compiler

Compiled 18458 to 11752 computations (36.3% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`sub-neg_binary64`
12×	`+-commutative_binary64`
11×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	109
1	59	109
2	91	109
3	108	109
4	117	109
5	118	109

Stop Event

1×

saturated

end124.0ms (2%)

Compiler: Compiled 390 to 174 computations (55.4% saved)

Details

analyze1.2s (19.3%)

sample1.1s (17.9%)

simplify25.0ms (0.4%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series54.0ms (0.9%)

rewrite65.0ms (1%)

simplify50.0ms (0.8%)

prune143.0ms (2.3%)

localize9.0ms (0.1%)

series129.0ms (2%)

rewrite79.0ms (1.2%)

simplify84.0ms (1.3%)

prune172.0ms (2.7%)

localize10.0ms (0.2%)

series116.0ms (1.9%)

rewrite65.0ms (1%)

simplify83.0ms (1.3%)

prune142.0ms (2.3%)

localize9.0ms (0.1%)

series195.0ms (3.1%)

rewrite137.0ms (2.2%)

simplify110.0ms (1.8%)

prune336.0ms (5.3%)

regimes1.8s (28.6%)

bsearch6.0ms (0.1%)

simplify5.0ms (0.1%)

end124.0ms (2%)

Profiling