Details

analyze1.4s (12.7%)

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
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.1%	87.7%	0.2%	13
21.4%	78.3%	0.4%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.4s (13.1%)

Results

842.0ms	6991×	body	128	valid
154.0ms	1254×	body	128	invalid
137.0ms	473×	body	512	valid
128.0ms	356×	body	1024	valid
81.0ms	373×	body	256	valid
29.0ms	63×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

930×	`fma-def_binary64`
302×	`unsub-neg_binary64`
210×	`distribute-rgt-in_binary64`
199×	`associate-+l-_binary64`
182×	`associate-+l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	24	17
2	53	17
3	165	17
4	619	17
5	2022	17

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

16.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.7b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	16.8b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

Compiler

Compiled 100 to 54 computations (46% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	16.6b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series81.0ms (0.7%)

Counts

2 → 108

Calls

2 calls:

56.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
25.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite57.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

264×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	257	27
2	3971	27

Stop Event

1×	node limit

Counts

2 → 74

Calls

2 calls:

55.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
55.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

simplify95.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

512×	`cancel-sign-sub-inv_binary64`
446×	`sub-neg_binary64`
349×	`associate-+r+_binary64`
269×	`+-commutative_binary64`
267×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	5085
1	840	5085
2	3617	5049

Stop Event

1×	node limit

Counts

182 → 142

prune135.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	132	10	142
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	134	10	144

Error

0.0b

Counts

144 → 10

Alt Table

Status	Error	Program
	39.2b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) 2)
	31.9b	(+.f64 (.f64 (/.f64 y z) x) (+.f64 t (-.f64 (.f64 (/.f64 a z) t) (+.f64 (/.f64 t (/.f64 z y)) (*.f64 (/.f64 a z) x)))))
	38.7b	(/.f64 (fma.f64 (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) (neg.f64 (.f64 x x))) (-.f64 (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) x))
	44.0b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
▶	15.1b	(+.f64 (.f64 (/.f64 z (-.f64 a z)) x) (-.f64 (+.f64 x (/.f64 t (/.f64 (-.f64 a z) y))) (+.f64 (.f64 (/.f64 t (-.f64 a z)) z) (*.f64 (/.f64 y (-.f64 a z)) x))))
	19.0b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))
	34.8b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	34.8b	(+.f64 x (fma.f64 (/.f64 z (-.f64 a z)) x (/.f64 (neg.f64 x) (/.f64 (-.f64 a z) y))))
	17.2b	(fma.f64 (-.f64 y z) (fma.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z)))) (cbrt.f64 (/.f64 t (-.f64 a z))) (neg.f64 (/.f64 x (-.f64 a z)))) x)
	37.6b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))

Compiler

Compiled 5058 to 1664 computations (67.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.5b	(*.f64 (/.f64 z (-.f64 a z)) x)
✓	6.1b	(*.f64 (/.f64 y (-.f64 a z)) x)
✓	6.2b	(/.f64 t (/.f64 (-.f64 a z) y))
✓	11.7b	(*.f64 (/.f64 t (-.f64 a z)) z)

series90.0ms (0.8%)

Counts

4 → 168

Calls

4 calls:

35.0ms	(/.f64 t (/.f64 (-.f64 a z) y))
24.0ms	(*.f64 (/.f64 y (-.f64 a z)) x)
15.0ms	(*.f64 (/.f64 t (-.f64 a z)) z)
15.0ms	(*.f64 (/.f64 z (-.f64 a z)) x)

rewrite37.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

172×	`add-sqr-sqrt_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`
159×	`add-cbrt-cube_binary64`
158×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	336	40

Stop Event

1×	node limit

Counts

4 → 130

Calls

4 calls:

35.0ms	(*.f64 (/.f64 z (-.f64 a z)) x)
35.0ms	(*.f64 (/.f64 y (-.f64 a z)) x)
35.0ms	(/.f64 t (/.f64 (-.f64 a z) y))
35.0ms	(*.f64 (/.f64 t (-.f64 a z)) z)

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

849×	`associate-/l*_binary64`
819×	`fma-def_binary64`
268×	`associate-/r/_binary64`
197×	`times-frac_binary64`
150×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	3504
1	542	3504
2	2079	2934

Stop Event

1×	node limit

Counts

298 → 207

prune200.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	208	9	217

Error

0.0b

Counts

217 → 9

Alt Table

Status	Error	Program
	39.2b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) 2)
	31.9b	(+.f64 (.f64 (/.f64 y z) x) (+.f64 t (-.f64 (.f64 (/.f64 a z) t) (+.f64 (/.f64 t (/.f64 z y)) (*.f64 (/.f64 a z) x)))))
	38.7b	(/.f64 (fma.f64 (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) (neg.f64 (.f64 x x))) (-.f64 (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) x))
	44.0b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
✓	15.1b	(+.f64 (.f64 (/.f64 z (-.f64 a z)) x) (-.f64 (+.f64 x (/.f64 t (/.f64 (-.f64 a z) y))) (+.f64 (.f64 (/.f64 t (-.f64 a z)) z) (*.f64 (/.f64 y (-.f64 a z)) x))))
	28.8b	(+.f64 (.f64 (/.f64 z (-.f64 a z)) x) (-.f64 (+.f64 x (/.f64 t (/.f64 (-.f64 a z) y))) (+.f64 (/.f64 (.f64 t z) a) (*.f64 (/.f64 y (-.f64 a z)) x))))
	34.8b	(+.f64 x (fma.f64 (/.f64 z (-.f64 a z)) x (/.f64 (neg.f64 x) (/.f64 (-.f64 a z) y))))
▶	17.2b	(fma.f64 (-.f64 y z) (fma.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z)))) (cbrt.f64 (/.f64 t (-.f64 a z))) (neg.f64 (/.f64 x (-.f64 a z)))) x)
	37.6b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))

Compiler

Compiled 8752 to 1805 computations (79.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z)))) (cbrt.f64 (/.f64 t (-.f64 a z))) (neg.f64 (/.f64 x (-.f64 a z))))
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z))))
✓	16.6b	(fma.f64 (-.f64 y z) (fma.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z)))) (cbrt.f64 (/.f64 t (-.f64 a z))) (neg.f64 (/.f64 x (-.f64 a z)))) x)
✓	18.3b	(cbrt.f64 (/.f64 t (-.f64 a z)))

series836.0ms (7.7%)

Counts

4 → 98

Calls

4 calls:

459.0ms	(fma.f64 (-.f64 y z) (fma.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z)))) (cbrt.f64 (/.f64 t (-.f64 a z))) (neg.f64 (/.f64 x (-.f64 a z)))) x)
228.0ms	(fma.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z)))) (cbrt.f64 (/.f64 t (-.f64 a z))) (neg.f64 (/.f64 x (-.f64 a z))))
76.0ms	(cbrt.f64 (/.f64 t (-.f64 a z)))
72.0ms	(*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z))))

rewrite66.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

286×	`log1p-udef_binary64`
169×	`add-sqr-sqrt_binary64`
160×	`add-cbrt-cube_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	332	60
2	4674	60

Stop Event

1×	node limit

Counts

4 → 99

Calls

4 calls:

64.0ms	(fma.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z)))) (cbrt.f64 (/.f64 t (-.f64 a z))) (neg.f64 (/.f64 x (-.f64 a z))))
64.0ms	(*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z))))
64.0ms	(fma.f64 (-.f64 y z) (fma.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z)))) (cbrt.f64 (/.f64 t (-.f64 a z))) (neg.f64 (/.f64 x (-.f64 a z)))) x)
64.0ms	(cbrt.f64 (/.f64 t (-.f64 a z)))

simplify98.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

803×	`fma-def_binary64`
382×	`times-frac_binary64`
293×	`*-commutative_binary64`
229×	`sqr-pow_binary64`
219×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	868	8799
1	2915	8787

Stop Event

1×	node limit

Counts

197 → 205

prune407.0ms (3.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	298	10	308

Error

0.0b

Counts

308 → 10

Alt Table

Status	Error	Program
	53.2b	(/.f64 (*.f64 x (-.f64 y a)) z)
	44.0b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	39.2b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) 2)
	31.9b	(+.f64 (.f64 (/.f64 y z) x) (+.f64 t (-.f64 (.f64 (/.f64 a z) t) (+.f64 (/.f64 t (/.f64 z y)) (*.f64 (/.f64 a z) x)))))
	38.7b	(/.f64 (fma.f64 (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) (neg.f64 (.f64 x x))) (-.f64 (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) x))
✓	15.1b	(+.f64 (.f64 (/.f64 z (-.f64 a z)) x) (-.f64 (+.f64 x (/.f64 t (/.f64 (-.f64 a z) y))) (+.f64 (.f64 (/.f64 t (-.f64 a z)) z) (*.f64 (/.f64 y (-.f64 a z)) x))))
▶	28.8b	(+.f64 (.f64 (/.f64 z (-.f64 a z)) x) (-.f64 (+.f64 x (/.f64 t (/.f64 (-.f64 a z) y))) (+.f64 (/.f64 (.f64 t z) a) (*.f64 (/.f64 y (-.f64 a z)) x))))
	34.8b	(+.f64 x (fma.f64 (/.f64 z (-.f64 a z)) x (/.f64 (neg.f64 x) (/.f64 (-.f64 a z) y))))
✓	17.2b	(fma.f64 (-.f64 y z) (fma.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z)))) (cbrt.f64 (/.f64 t (-.f64 a z))) (neg.f64 (/.f64 x (-.f64 a z)))) x)
	37.6b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))

Compiler

Compiled 18020 to 8930 computations (50.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.5b	(*.f64 (/.f64 z (-.f64 a z)) x)
✓	4.5b	(/.f64 (*.f64 t z) a)
	6.1b	(*.f64 (/.f64 y (-.f64 a z)) x)
	6.2b	(/.f64 t (/.f64 (-.f64 a z) y))

series13.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

13.0ms

(/.f64 (*.f64 t z) a)

rewrite36.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`log1p-expm1-u_binary64`
659×	`expm1-log1p-u_binary64`
367×	`log-prod_binary64`
119×	`expm1-udef_binary64`
119×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	125	7
2	1745	7

Stop Event

1×	node limit

Counts

1 → 46

Calls

1 calls:

35.0ms

(/.f64 (*.f64 t z) a)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

46 → 46

prune173.0ms (1.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	209	10	219

Error

0.0b

Counts

219 → 10

Alt Table

Status	Error	Program
	53.2b	(/.f64 (*.f64 x (-.f64 y a)) z)
	44.0b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	39.2b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) 2)
	31.9b	(+.f64 (.f64 (/.f64 y z) x) (+.f64 t (-.f64 (.f64 (/.f64 a z) t) (+.f64 (/.f64 t (/.f64 z y)) (*.f64 (/.f64 a z) x)))))
	38.7b	(/.f64 (fma.f64 (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) (neg.f64 (.f64 x x))) (-.f64 (/.f64 (.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)) x))
✓	15.1b	(+.f64 (.f64 (/.f64 z (-.f64 a z)) x) (-.f64 (+.f64 x (/.f64 t (/.f64 (-.f64 a z) y))) (+.f64 (.f64 (/.f64 t (-.f64 a z)) z) (*.f64 (/.f64 y (-.f64 a z)) x))))
✓	28.8b	(+.f64 (.f64 (/.f64 z (-.f64 a z)) x) (-.f64 (+.f64 x (/.f64 t (/.f64 (-.f64 a z) y))) (+.f64 (/.f64 (.f64 t z) a) (*.f64 (/.f64 y (-.f64 a z)) x))))
	34.8b	(+.f64 x (fma.f64 (/.f64 z (-.f64 a z)) x (/.f64 (neg.f64 x) (/.f64 (-.f64 a z) y))))
✓	17.2b	(fma.f64 (-.f64 y z) (fma.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 a z))) (cbrt.f64 (/.f64 t (-.f64 a z)))) (cbrt.f64 (/.f64 t (-.f64 a z))) (neg.f64 (/.f64 x (-.f64 a z)))) x)
	37.6b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))

Compiler

Compiled 8202 to 1692 computations (79.4% saved)

regimes5.4s (49.8%)

Accuracy

Total 2.2b remaining (93.7%)

Threshold costs 0b (0%)

Counts

216 → 7

Compiler

Compiled 35784 to 19362 computations (45.9% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

29×	`+-commutative_binary64`
23×	`*-commutative_binary64`
21×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	419
1	87	419
2	113	419
3	146	419
4	178	419
5	194	419
6	202	419
7	204	419

Stop Event

1×

saturated

end154.0ms (1.4%)

Compiler: Compiled 862 to 253 computations (70.6% saved)

Details

analyze1.4s (12.7%)

sample1.4s (13.1%)

simplify18.0ms (0.2%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series81.0ms (0.7%)

rewrite57.0ms (0.5%)

simplify95.0ms (0.9%)

prune135.0ms (1.2%)

localize16.0ms (0.2%)

series90.0ms (0.8%)

rewrite37.0ms (0.3%)

simplify60.0ms (0.6%)

prune200.0ms (1.8%)

localize14.0ms (0.1%)

series836.0ms (7.7%)

rewrite66.0ms (0.6%)

simplify98.0ms (0.9%)

prune407.0ms (3.8%)

localize16.0ms (0.1%)

series13.0ms (0.1%)

rewrite36.0ms (0.3%)

simplify7.0ms (0.1%)

prune173.0ms (1.6%)

regimes5.4s (49.8%)

bsearch10.0ms (0.1%)

simplify13.0ms (0.1%)

end154.0ms (1.4%)

Profiling