Details

analyze352.0ms (12.4%)

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)

sample970.0ms (34.3%)

Results

894.0ms	8256×	body	128	valid
27.0ms	256×	body	128	invalid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify22.0ms (0.8%)

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

prune4.0ms (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

0.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	17.1b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	1.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series68.0ms (2.4%)

Counts

2 → 60

Calls

2 calls:

55.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
14.0ms	(/.f64 v (+.f64 t1 u))

rewrite54.0ms (1.9%)

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

Calls

2 calls:

53.0ms	(/.f64 v (+.f64 t1 u))
53.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

simplify49.0ms (1.7%)

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

prune102.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	106	7	113

Error

0.5b

Counts

113 → 7

Alt Table

Status	Error	Program
▶	2.2b	(pow.f64 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)) -1)
	4.8b	(/.f64 (neg.f64 v) (*.f64 (+.f64 t1 u) (+.f64 1 (/.f64 u t1))))
	17.1b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	14.4b	(*.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (pow.f64 (/.f64 u t1) 2))) (+.f64 -1 (/.f64 u t1)))
	2.3b	(.f64 (pow.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) 2) (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (/.f64 1 (-.f64 -1 (/.f64 u t1)))))
	18.9b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 v (+.f64 t1 u)) 3)) (-.f64 -1 (/.f64 u t1)))
	31.1b	(*.f64 (/.f64 t1 u) (/.f64 (neg.f64 v) u))

Compiler

Compiled 2313 to 1099 computations (52.5% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 t1 u) v)
✓	0.7b	(pow.f64 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)) -1)
✓	1.5b	(*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v))

series90.0ms (3.2%)

Counts

3 → 96

Calls

3 calls:

58.0ms	(pow.f64 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)) -1)
23.0ms	(*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v))
8.0ms	(/.f64 (+.f64 t1 u) v)

rewrite60.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

628×	`prod-diff_binary64`
134×	`add-sqr-sqrt_binary64`
128×	`log1p-expm1-u_binary64`
128×	`expm1-log1p-u_binary64`
127×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	258	39
2	3886	39

Stop Event

1×	node limit

Counts

3 → 101

Calls

3 calls:

58.0ms	(/.f64 (+.f64 t1 u) v)
58.0ms	(pow.f64 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)) -1)
58.0ms	(*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v))

simplify55.0ms (2%)

Algorithm

1×	egg-herbie

Rules

892×	`cancel-sign-sub-inv_binary64`
611×	`fma-neg_binary64`
412×	`times-frac_binary64`
298×	`associate-/l*_binary64`
213×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	79	1917
1	242	1867
2	807	1777
3	3651	1777

Stop Event

1×	node limit

Counts

197 → 139

prune111.0ms (3.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	141	5	146

Error

0.5b

Counts

146 → 5

Alt Table

Status	Error	Program
	1.7b	(/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (/.f64 (+.f64 u t1) v))
	4.8b	(/.f64 (neg.f64 v) (*.f64 (+.f64 t1 u) (+.f64 1 (/.f64 u t1))))
	13.1b	(pow.f64 (neg.f64 (+.f64 (/.f64 (pow.f64 u 2) (.f64 t1 v)) (+.f64 (.f64 2 (/.f64 u v)) (/.f64 t1 v)))) -1)
	31.1b	(*.f64 (/.f64 t1 u) (/.f64 (neg.f64 v) u))
▶	1.6b	(/.f64 (/.f64 v (+.f64 u t1)) (-.f64 -1 (/.f64 u t1)))

Compiler

Compiled 2670 to 1317 computations (50.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 u t1))
✓	1.6b	(/.f64 (/.f64 v (+.f64 u t1)) (-.f64 -1 (/.f64 u t1)))

series66.0ms (2.3%)

Counts

2 → 72

Calls

2 calls:

52.0ms	(/.f64 (/.f64 v (+.f64 u t1)) (-.f64 -1 (/.f64 u t1)))
14.0ms	(/.f64 v (+.f64 u t1))

rewrite56.0ms (2%)

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

Calls

2 calls:

55.0ms	(/.f64 v (+.f64 u t1))
55.0ms	(/.f64 (/.f64 v (+.f64 u t1)) (-.f64 -1 (/.f64 u t1)))

simplify56.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	1683
1	223	1655
2	726	1595
3	3568	1595

Stop Event

1×	node limit

Counts

149 → 112

prune75.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	112	5	117

Error

0.5b

Counts

117 → 5

Alt Table

Status	Error	Program
▶	1.7b	(/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (/.f64 (+.f64 u t1) v))
	4.8b	(/.f64 (neg.f64 v) (*.f64 (+.f64 t1 u) (+.f64 1 (/.f64 u t1))))
	13.1b	(pow.f64 (neg.f64 (+.f64 (/.f64 (pow.f64 u 2) (.f64 t1 v)) (+.f64 (.f64 2 (/.f64 u v)) (/.f64 t1 v)))) -1)
	31.1b	(*.f64 (/.f64 t1 u) (/.f64 (neg.f64 v) u))
✓	1.6b	(/.f64 (/.f64 v (+.f64 u t1)) (-.f64 -1 (/.f64 u t1)))

Compiler

Compiled 2224 to 1047 computations (52.9% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 u t1) v)
✓	0.6b	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
✓	1.6b	(/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (/.f64 (+.f64 u t1) v))

series70.0ms (2.5%)

Counts

3 → 96

Calls

3 calls:

53.0ms	(/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (/.f64 (+.f64 u t1) v))
9.0ms	(/.f64 (+.f64 u t1) v)
8.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

rewrite63.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

664×	`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	36
1	274	33
2	4155	33

Stop Event

1×	node limit

Counts

3 → 101

Calls

3 calls:

61.0ms	(/.f64 (+.f64 u t1) v)
61.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
61.0ms	(/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (/.f64 (+.f64 u t1) v))

simplify72.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-neg_binary64`
459×	`times-frac_binary64`
318×	`associate-/l*_binary64`
298×	`distribute-neg-frac_binary64`
237×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1749
1	238	1721
2	782	1655
3	3729	1646

Stop Event

1×	node limit

Counts

197 → 141

prune97.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	141	5	146

Error

0.5b

Counts

146 → 5

Alt Table

Status	Error	Program
✓	1.7b	(/.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (/.f64 (+.f64 u t1) v))
	4.8b	(/.f64 (neg.f64 v) (*.f64 (+.f64 t1 u) (+.f64 1 (/.f64 u t1))))
	13.1b	(pow.f64 (neg.f64 (+.f64 (/.f64 (pow.f64 u 2) (.f64 t1 v)) (+.f64 (.f64 2 (/.f64 u v)) (/.f64 t1 v)))) -1)
	31.1b	(*.f64 (/.f64 t1 u) (/.f64 (neg.f64 v) u))
✓	1.6b	(/.f64 (/.f64 v (+.f64 u t1)) (-.f64 -1 (/.f64 u t1)))

Compiler

Compiled 2651 to 1271 computations (52.1% saved)

regimes235.0ms (8.3%)

Accuracy

Total 1.3b remaining (87.4%)

Threshold costs 0b (0%)

Counts

54 → 1

Compiler

Compiled 3446 to 2374 computations (31.1% 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

end71.0ms (2.5%)

Compiler: Compiled 107 to 71 computations (33.6% saved)

Details

analyze352.0ms (12.4%)

sample970.0ms (34.3%)

simplify22.0ms (0.8%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series68.0ms (2.4%)

rewrite54.0ms (1.9%)

simplify49.0ms (1.7%)

prune102.0ms (3.6%)

localize8.0ms (0.3%)

series90.0ms (3.2%)

rewrite60.0ms (2.1%)

simplify55.0ms (2%)

prune111.0ms (3.9%)

localize7.0ms (0.2%)

series66.0ms (2.3%)

rewrite56.0ms (2%)

simplify56.0ms (2%)

prune75.0ms (2.7%)

localize8.0ms (0.3%)

series70.0ms (2.5%)

rewrite63.0ms (2.2%)

simplify72.0ms (2.5%)

prune97.0ms (3.4%)

regimes235.0ms (8.3%)

simplify2.0ms (0.1%)

end71.0ms (2.5%)

Profiling