Details

analyze359.0ms (10.3%)

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%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample954.0ms (27.2%)

Results

916.0ms	8256×	body	128	valid
24.0ms	225×	body	128	invalid

Compiler

Compiled 32 to 18 computations (43.8% saved)

preprocess39.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

889×	`fma-def_binary64`
392×	`div-sub_binary64`
364×	`distribute-rgt-in_binary64`
359×	`fma-neg_binary64`
262×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	72
1	107	72
2	301	72
3	757	72
4	1547	72
5	2581	72
6	3584	72
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 8 computations (46.7% saved)

simplify22.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-def_binary64`
519×	`div-sub_binary64`
500×	`times-frac_binary64`
361×	`fma-neg_binary64`
269×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	87	18
3	235	18
4	454	18
5	721	18
6	928	18
7	1456	18
8	2429	16

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	16.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize14.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series67.0ms (1.9%)

Counts

2 → 60

Calls

18 calls:

17.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))	v	inf
15.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))	v	-inf
7.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))	v	0
4.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))	t1	0
2.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))	u	inf

rewrite61.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

646×	`prod-diff_binary64`
123×	`add-sqr-sqrt_binary64`
117×	`add-cbrt-cube_binary64`
117×	`log1p-expm1-u_binary64`
117×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	234	23
2	3673	23

Stop Event

1×	node limit

Counts

2 → 77

simplify52.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

870×	`fma-neg_binary64`
403×	`times-frac_binary64`
280×	`distribute-neg-frac_binary64`
278×	`associate-/l*_binary64`
205×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	1599
1	223	1571
2	726	1511
3	3566	1511

Stop Event

1×	node limit

Counts

137 → 111

prune90.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Error

0.0b

Counts

113 → 8

Alt Table

Status	Error	Program
	3.9b	(pow.f64 (cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 3)
	14.5b	(*.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (pow.f64 (/.f64 u t1) 2))) (+.f64 -1 (/.f64 u t1)))
✓	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	16.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	21.0b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 v (+.f64 t1 u)) 3)) (-.f64 -1 (/.f64 u t1)))
	32.6b	(*.f64 (/.f64 t1 u) (/.f64 (neg.f64 v) u))
▶	3.1b	(/.f64 (neg.f64 v) (+.f64 t1 (fma.f64 u 2 (*.f64 u (/.f64 u t1)))))
	21.7b	(pow.f64 (sqrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 2)

Compiler

Compiled 2313 to 1104 computations (52.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 u 2 (*.f64 u (/.f64 u t1)))
✓	0.1b	(*.f64 u (/.f64 u t1))
✓	3.1b	(/.f64 (neg.f64 v) (+.f64 t1 (fma.f64 u 2 (*.f64 u (/.f64 u t1)))))

series82.0ms (2.4%)

Counts

3 → 84

Calls

21 calls:

18.0ms	(/.f64 (neg.f64 v) (+.f64 t1 (fma.f64 u 2 (*.f64 u (/.f64 u t1)))))	v	inf
17.0ms	(/.f64 (neg.f64 v) (+.f64 t1 (fma.f64 u 2 (*.f64 u (/.f64 u t1)))))	v	0
16.0ms	(/.f64 (neg.f64 v) (+.f64 t1 (fma.f64 u 2 (*.f64 u (/.f64 u t1)))))	v	-inf
3.0ms	(/.f64 (neg.f64 v) (+.f64 t1 (fma.f64 u 2 (*.f64 u (/.f64 u t1)))))	t1	0
3.0ms	(/.f64 (neg.f64 v) (+.f64 t1 (fma.f64 u 2 (*.f64 u (/.f64 u t1)))))	t1	inf

rewrite59.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

688×	`prod-diff_binary64`
128×	`add-sqr-sqrt_binary64`
121×	`log1p-expm1-u_binary64`
121×	`expm1-log1p-u_binary64`
120×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	248	33
2	3633	33

Stop Event

1×	node limit

Counts

3 → 88

simplify48.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

786×	`cancel-sign-sub-inv_binary64`
479×	`fma-neg_binary64`
393×	`times-frac_binary64`
264×	`associate-/l*_binary64`
254×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	1464
1	166	1392
2	560	1392
3	2831	1392

Stop Event

1×	node limit

Counts

172 → 111

prune101.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	111	8	119

Error

0.0b

Counts

119 → 8

Alt Table

Status	Error	Program
▶	3.9b	(pow.f64 (cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 3)
	14.5b	(*.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (pow.f64 (/.f64 u t1) 2))) (+.f64 -1 (/.f64 u t1)))
✓	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	16.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	21.0b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 v (+.f64 t1 u)) 3)) (-.f64 -1 (/.f64 u t1)))
	32.6b	(*.f64 (/.f64 t1 u) (/.f64 (neg.f64 v) u))
✓	3.1b	(/.f64 (neg.f64 v) (+.f64 t1 (fma.f64 u 2 (*.f64 u (/.f64 u t1)))))
	21.7b	(pow.f64 (sqrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 2)

Compiler

Compiled 2212 to 1184 computations (46.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))
✓	0.4b	(pow.f64 (cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 3)
✓	3.1b	(/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))
✓	23.5b	(cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))))

series451.0ms (12.9%)

Counts

4 → 68

Calls

33 calls:

58.0ms	(pow.f64 (cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 3)	u	inf
46.0ms	(pow.f64 (cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 3)	t1	0
45.0ms	(pow.f64 (cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 3)	u	0
45.0ms	(pow.f64 (cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 3)	t1	inf
26.0ms	(cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))))	t1	0

rewrite76.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

637×	`prod-diff_binary64`
179×	`egg-rr`
137×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`
133×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	63
1	289	63
2	3973	63

Stop Event

1×	node limit

Counts

4 → 179

simplify44.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

539×	`associate-l_binary64`
492×	`fma-def_binary64`
430×	`times-frac_binary64`
304×	`associate-/l*_binary64`
247×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	1901
1	433	1824
2	1440	1805

Stop Event

1×	node limit

Counts

247 → 180

prune203.0ms (5.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	181	7	188

Error

0.0b

Counts

188 → 7

Alt Table

Status	Error	Program
▶	1.7b	(/.f64 1 (/.f64 (+.f64 t1 u) (/.f64 v (-.f64 -1 (/.f64 u t1)))))
	21.0b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 v (+.f64 t1 u)) 3)) (-.f64 -1 (/.f64 u t1)))
✓	3.9b	(pow.f64 (cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 3)
	14.5b	(*.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (pow.f64 (/.f64 u t1) 2))) (+.f64 -1 (/.f64 u t1)))
✓	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	16.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	3.1b	(/.f64 (neg.f64 v) (+.f64 t1 (fma.f64 u 2 (*.f64 u (/.f64 u t1)))))

Compiler

Compiled 4337 to 2447 computations (43.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (/.f64 (+.f64 t1 u) (/.f64 v (-.f64 -1 (/.f64 u t1)))))
✓	0.5b	(/.f64 (+.f64 t1 u) (/.f64 v (-.f64 -1 (/.f64 u t1))))
✓	3.2b	(/.f64 v (-.f64 -1 (/.f64 u t1)))

series106.0ms (3%)

Counts

3 → 108

Calls

27 calls:

23.0ms	(/.f64 1 (/.f64 (+.f64 t1 u) (/.f64 v (-.f64 -1 (/.f64 u t1)))))	v	inf
16.0ms	(/.f64 1 (/.f64 (+.f64 t1 u) (/.f64 v (-.f64 -1 (/.f64 u t1)))))	v	-inf
6.0ms	(/.f64 1 (/.f64 (+.f64 t1 u) (/.f64 v (-.f64 -1 (/.f64 u t1)))))	v	0
6.0ms	(/.f64 v (-.f64 -1 (/.f64 u t1)))	v	0
5.0ms	(/.f64 (+.f64 t1 u) (/.f64 v (-.f64 -1 (/.f64 u t1))))	v	inf

rewrite68.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`prod-diff_binary64`
140×	`add-sqr-sqrt_binary64`
133×	`add-cbrt-cube_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	274	42
2	4145	42

Stop Event

1×	node limit

Counts

3 → 126

simplify68.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

576×	`times-frac_binary64`
411×	`associate-/l*_binary64`
267×	`associate-/r*_binary64`
219×	`sub-neg_binary64`
210×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	2451
1	299	2401
2	1001	2212
3	4715	2203

Stop Event

1×	node limit

Counts

234 → 178

prune140.0ms (4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	178	7	185

Error

0.0b

Counts

185 → 7

Alt Table

Status	Error	Program
✓	1.7b	(/.f64 1 (/.f64 (+.f64 t1 u) (/.f64 v (-.f64 -1 (/.f64 u t1)))))
	21.0b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 v (+.f64 t1 u)) 3)) (-.f64 -1 (/.f64 u t1)))
	1.5b	(*.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (/.f64 1 (+.f64 u t1)))
✓	3.1b	(/.f64 (neg.f64 v) (+.f64 t1 (fma.f64 u 2 (*.f64 u (/.f64 u t1)))))
✓	3.9b	(pow.f64 (cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 3)
✓	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	16.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 3452 to 1745 computations (49.4% saved)

regimes243.0ms (6.9%)

Accuracy

Total 1.1b remaining (83.2%)

Threshold costs 0b (0%)

Counts

55 → 1

Compiler

Compiled 3262 to 2262 computations (30.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16
2	19	16
3	23	16
4	26	16
5	27	16

Stop Event

1×

saturated

end122.0ms (3.5%)

Stop Event

1×

fuel

Compiler

Compiled 139 to 91 computations (34.5% saved)

Details

analyze359.0ms (10.3%)

sample954.0ms (27.2%)

preprocess39.0ms (1.1%)

simplify22.0ms (0.6%)

prune3.0ms (0.1%)

localize14.0ms (0.4%)

series67.0ms (1.9%)

rewrite61.0ms (1.7%)

simplify52.0ms (1.5%)

prune90.0ms (2.6%)

localize8.0ms (0.2%)

series82.0ms (2.4%)

rewrite59.0ms (1.7%)

simplify48.0ms (1.4%)

prune101.0ms (2.9%)

localize9.0ms (0.3%)

series451.0ms (12.9%)

rewrite76.0ms (2.2%)

simplify44.0ms (1.3%)

prune203.0ms (5.8%)

localize8.0ms (0.2%)

series106.0ms (3%)

rewrite68.0ms (1.9%)

simplify68.0ms (1.9%)

prune140.0ms (4%)

regimes243.0ms (6.9%)

simplify2.0ms (0.1%)

end122.0ms (3.5%)

Profiling