Details

analyze1.7s (10.4%)

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
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
12.9%	79.1%	8%	12
15.8%	76.2%	8%	13
18.4%	73.6%	8%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample6.2s (37.8%)

Results

2.0s	1568×	body	8192	exit
1.5s	1852×	body	1024	valid
755.0ms	1408×	body	512	valid
749.0ms	3929×	body	128	valid
384.0ms	305×	body	2048	valid
264.0ms	762×	body	256	valid
263.0ms	1716×	body	128	invalid
152.0ms	281×	body	512	invalid
128.0ms	220×	body	1024	invalid
45.0ms	153×	body	256	invalid

Compiler

Compiled 36 to 26 computations (27.8% saved)

preprocess61.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

471×	`fma-neg_binary64`
400×	`fma-def_binary64`
360×	`sub-neg_binary64`
211×	`cancel-sign-sub-inv_binary64`
190×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	140
1	94	126
2	235	119
3	504	119
4	1097	98
5	2393	98
6	3747	98
7	4924	98
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
369×	`fma-neg_binary64`
355×	`div-sub_binary64`
287×	`sub-neg_binary64`
210×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	23	18
2	48	17
3	96	17
4	206	14
5	423	14
6	722	14
7	906	14
8	1020	14
9	1231	14
10	1745	14
11	3240	14
12	4174	14
13	4800	14

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.0b	(*.f64 y (expm1.f64 z))
✓	4.9b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.3s (7.8%)

Counts

4 → 132

Calls

33 calls:

142.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)	t	-inf
135.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)	t	inf
119.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)	t	0
118.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)	z	-inf
117.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)	z	inf

rewrite89.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

727×	`prod-diff_binary64`
198×	`expm1-udef_binary64`
198×	`log1p-udef_binary64`
159×	`egg-rr`
114×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	210	39
2	2845	39

Stop Event

1×	node limit

Counts

4 → 159

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

480×	`sub-neg_binary64`
305×	`fma-def_binary64`
275×	`+-commutative_binary64`
275×	`associate-+r+_binary64`
236×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	3764
1	1042	3317
2	4074	3303

Stop Event

1×	node limit

Counts

291 → 265

prune268.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	260	5	265
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	260	6	266

Error

Counts

266 → 6

Alt Table

Status	Error	Program
	29.4b	(-.f64 x (fma.f64 1/3 (/.f64 (pow.f64 y 3) (/.f64 t (pow.f64 z 3))) (+.f64 (fma.f64 1/2 (.f64 (/.f64 y t) (.f64 z z)) (.f64 (/.f64 y t) z)) (fma.f64 1/6 (.f64 (/.f64 y t) (pow.f64 z 3)) (.f64 -1/2 (+.f64 (.f64 (/.f64 y (/.f64 t y)) (*.f64 z z)) (/.f64 y (/.f64 (/.f64 t (pow.f64 z 3)) y))))))))
	1.3b	(-.f64 x (pow.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 3))
▶	1.3b	(-.f64 x (.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (cbrt.f64 t))))
✓	1.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	4.9b	(-.f64 x (/.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 2))) t))
	41.3b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) 3)) (fma.f64 x x (.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) (+.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) x))))

Compiler

Compiled 9040 to 3782 computations (58.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 t) 2)
✓	0.6b	(cbrt.f64 t)
✓	2.1b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (cbrt.f64 t))
✓	3.1b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (cbrt.f64 t)))

series1.1s (6.5%)

Counts

4 → 60

Calls

24 calls:

214.0ms	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (cbrt.f64 t)))	t	-inf
138.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (cbrt.f64 t))	z	-inf
132.0ms	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (cbrt.f64 t)))	t	inf
129.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (cbrt.f64 t))	z	inf
121.0ms	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (cbrt.f64 t)))	z	inf

rewrite63.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`prod-diff_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
217×	`log-pow_binary64`
133×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	287	33
2	3517	33

Stop Event

1×	node limit

Counts

4 → 133

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

628×	`times-frac_binary64`
373×	`fma-neg_binary64`
359×	`fma-def_binary64`
299×	`associate-r_binary64`
277×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	2874
1	1063	2486
2	4395	2482

Stop Event

1×	node limit

Counts

193 → 200

prune267.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	223	6	229

Error

Counts

229 → 6

Alt Table

Status	Error	Program
	22.3b	(-.f64 x (cbrt.f64 (/.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3) (pow.f64 t 3))))
▶	1.3b	(-.f64 x (pow.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 3))
✓	1.3b	(-.f64 x (.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (cbrt.f64 t))))
✓	1.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	25.7b	(-.f64 x (+.f64 (.f64 (/.f64 y t) z) (.f64 1/2 (-.f64 (.f64 (/.f64 y t) (.f64 z z)) (.f64 (/.f64 (.f64 y y) t) (*.f64 z z))))))
	4.9b	(-.f64 x (/.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 2))) t))

Compiler

Compiled 6840 to 3657 computations (46.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (expm1.f64 z))
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 3)
	4.9b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
✓	19.2b	(cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

series1.7s (10.5%)

Counts

2 → 32

Calls

18 calls:

406.0ms	(pow.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 3)	z	0
350.0ms	(pow.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 3)	y	0
175.0ms	(pow.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 3)	z	inf
162.0ms	(pow.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 3)	z	-inf
153.0ms	(cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))	z	-inf

rewrite56.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

905×	`expm1-log1p-u_binary64`
904×	`log1p-expm1-u_binary64`
213×	`prod-diff_binary64`
99×	`add-sqr-sqrt_binary64`
92×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	221	24
2	2515	24

Stop Event

1×	node limit

Counts

2 → 77

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-def_binary64`
270×	`cancel-sign-sub-inv_binary64`
256×	`distribute-rgt-in_binary64`
230×	`distribute-lft-in_binary64`
128×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2453
1	557	2181
2	2093	2111

Stop Event

1×	node limit

Counts

109 → 113

prune273.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	206	6	212

Error

Counts

212 → 6

Alt Table

Status	Error	Program
	22.3b	(-.f64 x (cbrt.f64 (/.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3) (pow.f64 t 3))))
✓	1.3b	(-.f64 x (pow.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 3))
✓	1.3b	(-.f64 x (.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (cbrt.f64 t))))
✓	1.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	25.7b	(-.f64 x (+.f64 (.f64 (/.f64 y t) z) (.f64 1/2 (-.f64 (.f64 (/.f64 y t) (.f64 z z)) (.f64 (/.f64 (.f64 y y) t) (*.f64 z z))))))
▶	4.9b	(-.f64 x (/.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 2))) t))

Compiler

Compiled 6667 to 3640 computations (45.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 2)
✓	4.9b	(/.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 2))) t)
✓	14.6b	(cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
✓	28.7b	(cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 2))

series1.9s (11.4%)

Counts

4 → 92

Calls

27 calls:

166.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 2))	z	inf
159.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 2))	z	-inf
153.0ms	(cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))	z	inf
142.0ms	(cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))	z	-inf
134.0ms	(/.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 2))) t)	t	-inf

rewrite62.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

561×	`log-prod_binary64`
225×	`prod-diff_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
187×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	60
1	261	45
2	3034	45

Stop Event

1×	node limit

Counts

4 → 121

simplify106.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
415×	`associate-/r*_binary64`
290×	`times-frac_binary64`
234×	`associate-/l*_binary64`
206×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	633	8640
1	2251	7631

Stop Event

1×	node limit

Counts

213 → 225

prune344.0ms (2.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	225	6	231

Error

Counts

231 → 6

Alt Table

Status	Error	Program
	22.3b	(-.f64 x (cbrt.f64 (/.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3) (pow.f64 t 3))))
✓	1.3b	(-.f64 x (pow.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 3))
✓	1.3b	(-.f64 x (.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (cbrt.f64 t))))
✓	1.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	25.7b	(-.f64 x (+.f64 (.f64 (/.f64 y t) z) (.f64 1/2 (-.f64 (.f64 (/.f64 y t) (.f64 z z)) (.f64 (/.f64 (.f64 y y) t) (*.f64 z z))))))
✓	4.9b	(-.f64 x (/.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 2))) t))

Compiler

Compiled 13178 to 7568 computations (42.6% saved)

regimes558.0ms (3.4%)

Accuracy

Total 0.8b remaining (78.3%)

Threshold costs 0.8b (78.3%)

Counts

66 → 1

Compiler

Compiled 12703 to 8459 computations (33.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
2	20	14
3	24	14
4	27	14
5	28	14

Stop Event

1×

saturated

end94.0ms (0.6%)

Stop Event

1×

fuel

Compiler

Compiled 148 to 98 computations (33.8% saved)

Details

analyze1.7s (10.4%)

sample6.2s (37.8%)

preprocess61.0ms (0.4%)

simplify50.0ms (0.3%)

prune5.0ms (0%)

localize7.0ms (0%)

series1.3s (7.8%)

rewrite89.0ms (0.5%)

simplify82.0ms (0.5%)

prune268.0ms (1.6%)

localize14.0ms (0.1%)

series1.1s (6.5%)

rewrite63.0ms (0.4%)

simplify78.0ms (0.5%)

prune267.0ms (1.6%)

localize10.0ms (0.1%)

series1.7s (10.5%)

rewrite56.0ms (0.3%)

simplify56.0ms (0.3%)

prune273.0ms (1.7%)

localize13.0ms (0.1%)

series1.9s (11.4%)

rewrite62.0ms (0.4%)

simplify106.0ms (0.6%)

prune344.0ms (2.1%)

regimes558.0ms (3.4%)

simplify2.0ms (0%)

end94.0ms (0.6%)

Profiling