Details

analyze447.0ms (6.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	87.4%	12.6%	5
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
12.5%	56.2%	31.4%	8
14%	48.4%	37.6%	9
21.1%	41.3%	37.6%	10
26.9%	32.4%	40.7%	11
28.7%	27.5%	43.8%	12
33.4%	22.7%	43.8%	13
37.2%	17.4%	45.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (17.5%)

Results

1.0s	8256×	body	128	valid
94.0ms	828×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess55.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

455×	`div-sub_binary64`
369×	`fma-neg_binary64`
308×	`fma-def_binary64`
266×	`cancel-sign-sub-inv_binary64`
260×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	48
1	42	48
2	65	48
3	123	48
4	354	48
5	836	48
6	1839	48
7	2959	48
8	4118	48
9	4864	48
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1663×	`fma-def_binary64`
528×	`fma-neg_binary64`
288×	`distribute-rgt-in_binary64`
230×	`unsub-neg_binary64`
193×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	15	12
2	23	12
3	39	12
4	98	12
5	231	12
6	474	12
7	898	12
8	1256	12
9	2133	12
10	3636	12
11	4010	12
12	4136	12
13	4175	12
14	4189	12

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

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

15.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.3b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))

Compiler

Compiled 41 to 23 computations (43.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
✓	15.0b	(log.f64 (/.f64 x y))

series608.0ms (9.4%)

Counts

2 → 60

Calls

15 calls:

68.0ms	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))	y	-inf
66.0ms	(log.f64 (/.f64 x y))	x	0
61.0ms	(log.f64 (/.f64 x y))	x	-inf
60.0ms	(log.f64 (/.f64 x y))	x	inf
57.0ms	(log.f64 (/.f64 x y))	y	-inf

rewrite72.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

710×	`log1p-expm1-u_binary64`
710×	`expm1-log1p-u_binary64`
191×	`egg-rr`
165×	`prod-diff_binary64`
137×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	165	16
2	2154	16

Stop Event

1×	node limit

Counts

2 → 191

simplify98.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

492×	`fma-neg_binary64`
410×	`unsub-neg_binary64`
305×	`sub-neg_binary64`
289×	`distribute-rgt-in_binary64`
230×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	558
1	125	540
2	268	540
3	669	540
4	2021	540
5	3640	540
6	4344	540
7	4799	540
8	4924	540
9	4973	540
10	4981	540

Stop Event

1×	node limit

Counts

251 → 209

prune125.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	203	6	209
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	203	7	210

Error

0.0b

Counts

210 → 7

Alt Table

Status	Error	Program
	31.4b	(-.f64 (+.f64 (.f64 (log.f64 (/.f64 -1 y)) x) (.f64 (log.f64 (neg.f64 x)) x)) z)
✓	15.3b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
	32.9b	(fma.f64 x (/.f64 (-.f64 (pow.f64 (log.f64 x) 3) (pow.f64 (log.f64 y) 3)) (+.f64 (.f64 (log.f64 x) (log.f64 x)) (+.f64 (.f64 (log.f64 y) (log.f64 y)) (*.f64 (log.f64 x) (log.f64 y))))) (neg.f64 z))
	43.5b	(fma.f64 x (expm1.f64 (log1p.f64 (log.f64 (/.f64 x y)))) (neg.f64 z))
▶	15.4b	(fma.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y)))) (neg.f64 z))
	33.2b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
	15.5b	(fma.f64 x (cbrt.f64 (pow.f64 (log.f64 (/.f64 x y)) 3)) (neg.f64 z))

Compiler

Compiled 4827 to 1425 computations (70.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y))))
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 x y)) 2)
✓	3.7b	(log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2))
✓	15.3b	(cbrt.f64 (/.f64 x y))

series205.0ms (3.2%)

Counts

4 → 0

Calls

24 calls:

29.0ms	(pow.f64 (cbrt.f64 (/.f64 x y)) 2)	y	-inf
27.0ms	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y))))	y	-inf
24.0ms	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y))))	x	-inf
20.0ms	(log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2))	y	-inf
20.0ms	(pow.f64 (cbrt.f64 (/.f64 x y)) 2)	x	-inf

rewrite62.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`prod-diff_binary64`
245×	`fma-def_binary64`
172×	`expm1-udef_binary64`
172×	`log1p-udef_binary64`
152×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	213	32
2	2706	32

Stop Event

1×	node limit

Counts

4 → 141

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

141 → 141

prune170.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	171	3	174
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	174	7	181

Error

Counts

181 → 7

Alt Table

Status	Error	Program
	31.4b	(-.f64 (+.f64 (.f64 (log.f64 (/.f64 -1 y)) x) (.f64 (log.f64 (neg.f64 x)) x)) z)
✓	15.3b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
✓	15.4b	(fma.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y)))) (neg.f64 z))
	33.2b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
▶	15.5b	(fma.f64 x (fma.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) 2) (*.f64 2 (log.f64 (cbrt.f64 (/.f64 x y))))) (neg.f64 z))
	15.6b	(fma.f64 x (fma.f64 (cbrt.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 x y))))) (pow.f64 (cbrt.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 x y))))) 2) (log.f64 (cbrt.f64 (/.f64 x y)))) (neg.f64 z))
	15.5b	(fma.f64 x (/.f64 (fma.f64 8 (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 3) (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 3)) (-.f64 (fma.f64 4 (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 2) (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 2)) (*.f64 2 (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 2)))) (neg.f64 z))

Compiler

Compiled 4023 to 1435 computations (64.3% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) 2) (*.f64 2 (log.f64 (cbrt.f64 (/.f64 x y)))))
✓	0.5b	(pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) 2)
✓	0.5b	(cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y))))
	15.3b	(cbrt.f64 (/.f64 x y))

series412.0ms (6.4%)

Counts

3 → 0

Calls

18 calls:

55.0ms	(fma.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) 2) (*.f64 2 (log.f64 (cbrt.f64 (/.f64 x y)))))	y	-inf
55.0ms	(pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) 2)	y	-inf
53.0ms	(fma.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) 2) (*.f64 2 (log.f64 (cbrt.f64 (/.f64 x y)))))	x	-inf
32.0ms	(pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) 2)	x	-inf
26.0ms	(cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y))))	x	-inf

rewrite63.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

893×	`log1p-expm1-u_binary64`
893×	`expm1-log1p-u_binary64`
304×	`prod-diff_binary64`
103×	`add-sqr-sqrt_binary64`
97×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	59
1	221	29
2	2591	29

Stop Event

1×	node limit

Counts

3 → 79

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

79 → 79

prune218.0ms (3.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	202	6	208

Error

Counts

208 → 6

Alt Table

Status	Error	Program
	31.4b	(-.f64 (+.f64 (.f64 (log.f64 (/.f64 -1 y)) x) (.f64 (log.f64 (neg.f64 x)) x)) z)
✓	15.3b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
✓	15.4b	(fma.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y)))) (neg.f64 z))
	33.2b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
	15.6b	(fma.f64 x (fma.f64 (cbrt.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 x y))))) (pow.f64 (cbrt.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 x y))))) 2) (log.f64 (cbrt.f64 (/.f64 x y)))) (neg.f64 z))
▶	15.5b	(fma.f64 x (fma.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) 2) (*.f64 2 (log.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 x y))) 3)))) (neg.f64 z))

Compiler

Compiled 5894 to 1906 computations (67.7% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y))))
✓	0.5b	(cbrt.f64 (cbrt.f64 (/.f64 x y)))
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 x y))) 3)
	15.3b	(cbrt.f64 (/.f64 x y))

series1.2s (19.2%)

Counts

2 → 48

Calls

12 calls:

206.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 x y))) 3)	x	-inf
189.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 x y))) 3)	y	-inf
182.0ms	(cbrt.f64 (cbrt.f64 (/.f64 x y)))	x	-inf
178.0ms	(cbrt.f64 (cbrt.f64 (/.f64 x y)))	y	-inf
68.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 x y))) 3)	x	inf

rewrite46.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

653×	`log1p-expm1-u_binary64`
653×	`expm1-log1p-u_binary64`
328×	`log-prod_binary64`
123×	`expm1-udef_binary64`
123×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	163	14
2	1819	14

Stop Event

1×	node limit

Counts

2 → 62

simplify53.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

832×	`fma-def_binary64`
362×	`associate-l_binary64`
308×	`associate-r_binary64`
196×	`unsub-neg_binary64`
185×	`exp-sum_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	44	872
1	119	872
2	268	872
3	845	784
4	3343	768

Stop Event

1×	node limit

Counts

110 → 76

prune221.0ms (3.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	221	6	227

Error

Counts

227 → 6

Alt Table

Status	Error	Program
	31.4b	(-.f64 (+.f64 (.f64 (log.f64 (/.f64 -1 y)) x) (.f64 (log.f64 (neg.f64 x)) x)) z)
✓	15.3b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
✓	15.4b	(fma.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y)))) (neg.f64 z))
	33.2b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
	15.6b	(fma.f64 x (fma.f64 (cbrt.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 x y))))) (pow.f64 (cbrt.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 x y))))) 2) (log.f64 (cbrt.f64 (/.f64 x y)))) (neg.f64 z))
✓	15.5b	(fma.f64 x (fma.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 x y)))) 2) (*.f64 2 (log.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 x y))) 3)))) (neg.f64 z))

Compiler

Compiled 7516 to 2904 computations (61.4% saved)

regimes958.0ms (14.8%)

Accuracy

Total 0.3b remaining (78.3%)

Threshold costs 0.3b (78.3%)

Counts

102 → 2

Compiler

Compiled 12293 to 7128 computations (42% saved)

bsearch44.0ms (0.7%)

Algorithm

1×	binary-search

Calls

1 calls:

40.0ms

Steps

Iters	Point		Range
-3.99757940389e-311	∈ [	-1.2671179016545378e-306	,	2.8343510777288117e-297	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	34	38
2	45	38
3	51	38
4	52	38

Stop Event

1×

saturated

end100.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 179 to 109 computations (39.1% saved)

Details

analyze447.0ms (6.9%)

sample1.1s (17.5%)

preprocess55.0ms (0.8%)

simplify51.0ms (0.8%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series608.0ms (9.4%)

rewrite72.0ms (1.1%)

simplify98.0ms (1.5%)

prune125.0ms (1.9%)

localize12.0ms (0.2%)

series205.0ms (3.2%)

rewrite62.0ms (1%)

simplify9.0ms (0.1%)

prune170.0ms (2.6%)

localize21.0ms (0.3%)

series412.0ms (6.4%)

rewrite63.0ms (1%)

simplify8.0ms (0.1%)

prune218.0ms (3.4%)

localize18.0ms (0.3%)

series1.2s (19.2%)

rewrite46.0ms (0.7%)

simplify53.0ms (0.8%)

prune221.0ms (3.4%)

regimes958.0ms (14.8%)

bsearch44.0ms (0.7%)

simplify5.0ms (0.1%)

end100.0ms (1.6%)

Profiling