Details

analyze638.0ms (6.1%)

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)

sample1.8s (17.5%)

Results

1.7s	8256×	body	128	valid
44.0ms	257×	body	128	invalid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

prune6.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.7b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	15.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -1 (/.f64 u t1))
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	1.7b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series155.0ms (1.5%)

Counts

3 → 84

Calls

3 calls:

118.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
29.0ms	(/.f64 v (+.f64 t1 u))
8.0ms	(-.f64 -1 (/.f64 u t1))

rewrite103.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

646×	`prod-diff_binary64`
223×	`log1p-udef_binary64`
123×	`add-sqr-sqrt_binary64`
117×	`log1p-expm1-u_binary64`
117×	`expm1-log1p-u_binary64`

Counts

3 → 107

Calls

3 calls:

100.0ms	(-.f64 -1 (/.f64 u t1))
100.0ms	(/.f64 v (+.f64 t1 u))
100.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	234	30
2	3505	30
3	5206	30
0	0	0
1	0	0

simplify98.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

875×	`fma-neg_binary64`
405×	`times-frac_binary64`
343×	`distribute-rgt-neg-in_binary64`
279×	`associate-/l*_binary64`
279×	`distribute-neg-frac_binary64`

Counts

191 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	75	1782
1	231	1718
2	728	1658
3	3215	1658
4	4984	1658

prune248.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	142	6	148

Error

0.2b

Counts

148 → 6

Alt Table

Status	Error	Program
	15.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	21.8b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 2)
	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 3))
	13.1b	(*.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (pow.f64 (/.f64 u t1) 2))) (+.f64 -1 (/.f64 u t1)))
▶	1.8b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
	2.3b	(.f64 v (.f64 (/.f64 1 (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 2866 to 1294 computations (54.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 -1 (/.f64 u t1))
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.6b	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
✓	1.5b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

series138.0ms (1.3%)

Counts

2 → 60

Calls

2 calls:

121.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
17.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

rewrite99.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

637×	`prod-diff_binary64`
138×	`add-sqr-sqrt_binary64`
130×	`log1p-expm1-u_binary64`
130×	`expm1-log1p-u_binary64`
128×	`add-cbrt-cube_binary64`

Counts

2 → 76

Calls

2 calls:

96.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
96.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	272	26
2	3771	26
3	5024	26
0	0	0
1	0	0

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
459×	`times-frac_binary64`
315×	`associate-/l*_binary64`
298×	`distribute-neg-frac_binary64`
296×	`distribute-rgt-neg-in_binary64`

Counts

136 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	1461
1	231	1433
2	756	1367
3	3354	1358
4	5074	1358

prune318.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	194	7	201

Error

0.2b

Counts

201 → 7

Alt Table

Status	Error	Program
✓	1.8b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
	2.1b	(/.f64 v (/.f64 (+.f64 t1 u) (/.f64 1 (-.f64 -1 (/.f64 u t1)))))
	15.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	21.8b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 2)
▶	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 3))
	13.1b	(*.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (pow.f64 (/.f64 u t1) 2))) (+.f64 -1 (/.f64 u t1)))
	32.7b	(/.f64 (/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (sqrt.f64 (+.f64 t1 u))) (sqrt.f64 (+.f64 t1 u)))

Compiler

Compiled 3754 to 1786 computations (52.4% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.3b	(pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 3)
✓	1.7b	(/.f64 (/.f64 v (+.f64 t1 u)) (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 3))
✓	8.6b	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))

series3.0s (28.8%)

Counts

3 → 84

Calls

3 calls:

2.7s	(pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 3)
227.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 3))
82.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))

rewrite110.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

658×	`prod-diff_binary64`
141×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`
133×	`add-cbrt-cube_binary64`

Counts

3 → 107

Calls

3 calls:

106.0ms	(pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 3)
106.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 3))
106.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	281	32
2	3957	32
3	5203	32
0	0	0
1	0	0

simplify116.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

848×	`associate-/l*_binary64`
580×	`associate-/r*_binary64`
415×	`fma-def_binary64`
254×	`associate-/r/_binary64`
157×	`cancel-sign-sub-inv_binary64`

Counts

191 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2811
1	532	2595
2	1735	2329
3	5023	2329

prune361.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	221	7	228

Error

0.2b

Counts

228 → 7

Alt Table

Status	Error	Program
✓	1.8b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
▶	2.1b	(/.f64 v (/.f64 (+.f64 t1 u) (/.f64 1 (-.f64 -1 (/.f64 u t1)))))
	15.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	21.8b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 2)
✓	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 3))
	13.1b	(*.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (pow.f64 (/.f64 u t1) 2))) (+.f64 -1 (/.f64 u t1)))
	32.7b	(/.f64 (/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (sqrt.f64 (+.f64 t1 u))) (sqrt.f64 (+.f64 t1 u)))

Compiler

Compiled 5341 to 2798 computations (47.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 -1 (/.f64 u t1))
✓	0.1b	(/.f64 (+.f64 t1 u) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
	0.6b	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
✓	2.1b	(/.f64 v (/.f64 (+.f64 t1 u) (/.f64 1 (-.f64 -1 (/.f64 u t1)))))

series394.0ms (3.8%)

Counts

2 → 60

Calls

2 calls:

376.0ms	(/.f64 v (/.f64 (+.f64 t1 u) (/.f64 1 (-.f64 -1 (/.f64 u t1)))))
18.0ms	(/.f64 (+.f64 t1 u) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

rewrite119.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

661×	`prod-diff_binary64`
139×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`
129×	`add-cbrt-cube_binary64`

Counts

2 → 81

Calls

2 calls:

116.0ms	(/.f64 (+.f64 t1 u) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
116.0ms	(/.f64 v (/.f64 (+.f64 t1 u) (/.f64 1 (-.f64 -1 (/.f64 u t1)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	274	29
2	3809	29
3	5120	29
0	0	0
1	0	0

simplify114.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

869×	`cancel-sign-sub-inv_binary64`
591×	`fma-neg_binary64`
406×	`times-frac_binary64`
277×	`associate-/l*_binary64`
207×	`associate-/r*_binary64`

Counts

141 → 111

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	1341
1	209	1277
2	686	1277
3	2924	1277
4	4929	1277
5	5047	1277

prune519.0ms (4.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	187	6	193

Error

0.2b

Counts

193 → 6

Alt Table

Status	Error	Program
	15.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	21.8b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 2)
✓	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 3))
	13.1b	(*.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (pow.f64 (/.f64 u t1) 2))) (+.f64 -1 (/.f64 u t1)))
	2.8b	(pow.f64 (cbrt.f64 (/.f64 v (*.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1))))) 3)
✓	1.8b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

Compiler

Compiled 3383 to 1717 computations (49.2% saved)

regimes1.8s (16.7%)

Accuracy

Total 1.1b remaining (84.2%)

Threshold costs 0b (0%)

Counts

189 → 1

Compiler

Compiled 12406 to 8430 computations (32% saved)

simplify4.0ms (0%)

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
6	27	16

end79.0ms (0.8%)

Compiler: Compiled 132 to 87 computations (34.1% saved)

Details

analyze638.0ms (6.1%)

sample1.8s (17.5%)

simplify79.0ms (0.7%)

prune6.0ms (0.1%)

localize13.0ms (0.1%)

series155.0ms (1.5%)

rewrite103.0ms (1%)

simplify98.0ms (0.9%)

prune248.0ms (2.4%)

localize16.0ms (0.1%)

series138.0ms (1.3%)

rewrite99.0ms (0.9%)

simplify104.0ms (1%)

prune318.0ms (3%)

localize26.0ms (0.2%)

series3.0s (28.8%)

rewrite110.0ms (1.1%)

simplify116.0ms (1.1%)

prune361.0ms (3.4%)

localize15.0ms (0.1%)

series394.0ms (3.8%)

rewrite119.0ms (1.1%)

simplify114.0ms (1.1%)

prune519.0ms (4.9%)

regimes1.8s (16.7%)

simplify4.0ms (0%)

end79.0ms (0.8%)

Profiling