Details

analyze1.4s (26%)

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
0%	99.8%	0.2%	9
0.4%	99.4%	0.2%	10
4.3%	95.5%	0.2%	11
6.4%	93.3%	0.2%	12
7.9%	91.9%	0.2%	13
13.7%	86%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.2s (21.2%)

Results

1.0s	8256×	body	128	valid
62.0ms	488×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify25.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
362×	`div-sub_binary64`
353×	`cancel-sign-sub-inv_binary64`
300×	`sub-neg_binary64`
240×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	28	19
2	67	19
3	166	17
4	423	17
5	1175	17
6	3293	17

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

1.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.8b	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)
	2.2b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 100 to 64 computations (36% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 t (+.f64 z -1)))
✓	1.8b	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)

series69.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

48.0ms	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)
21.0ms	(/.f64 a (-.f64 t (+.f64 z -1)))

rewrite59.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

271×	`fma-neg_binary64`
261×	`expm1-udef_binary64`
261×	`log1p-udef_binary64`
143×	`add-sqr-sqrt_binary64`
136×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	271	27
2	3974	27

Stop Event

1×	node limit

Counts

2 → 58

Calls

2 calls:

58.0ms	(/.f64 a (-.f64 t (+.f64 z -1)))
58.0ms	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)

simplify79.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

598×	`cancel-sign-sub-inv_binary64`
371×	`times-frac_binary64`
351×	`sub-neg_binary64`
318×	`associate-+r+_binary64`
270×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	3917
1	943	3913
2	3940	3898

Stop Event

1×	node limit

Counts

154 → 133

prune137.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	131	4	135

Error

Counts

135 → 4

Alt Table

Status	Error	Program
	2.2b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	1.8b	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)
	2.2b	(fma.f64 (pow.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) -1) (-.f64 z y) x)
	12.1b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 4216 to 2124 computations (49.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 (-.f64 t z) 1))
✓	0.2b	(*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))
✓	1.8b	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)

series80.0ms (1.5%)

Counts

3 → 120

Calls

3 calls:

48.0ms	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)
23.0ms	(*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))
10.0ms	(/.f64 1 (+.f64 (-.f64 t z) 1))

rewrite63.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

919×	`prod-diff_binary64`
150×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
142×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	292	37
2	4091	37

Stop Event

1×	node limit

Counts

3 → 74

Calls

3 calls:

61.0ms	(/.f64 1 (+.f64 (-.f64 t z) 1))
61.0ms	(*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))
61.0ms	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

429×	`associate-+r+_binary64`
407×	`times-frac_binary64`
354×	`+-commutative_binary64`
309×	`associate-+l+_binary64`
263×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	360	4851
1	1172	4843
2	4864	4843

Stop Event

1×	node limit

Counts

194 → 175

prune167.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	175	4	179

Error

Counts

179 → 4

Alt Table

Status	Error	Program
▶	2.2b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	1.8b	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)
	2.2b	(fma.f64 (pow.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) -1) (-.f64 z y) x)
	12.1b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 5372 to 2824 computations (47.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
✓	8.8b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series120.0ms (2.2%)

Counts

3 → 144

Calls

3 calls:

64.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
45.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
11.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite82.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

291×	`log1p-udef_binary64`
162×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`
156×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	309	45
2	4927	45

Stop Event

1×	node limit

Counts

3 → 118

Calls

3 calls:

79.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
79.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)
79.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

454×	`associate-+r+_binary64`
389×	`times-frac_binary64`
356×	`+-commutative_binary64`
343×	`associate-+l+_binary64`
263×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	355	5790
1	1325	5790

Stop Event

1×	node limit

Counts

262 → 219

prune240.0ms (4.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	219	4	223

Error

Counts

223 → 4

Alt Table

Status	Error	Program
✓	2.2b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	1.8b	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)
▶	2.2b	(fma.f64 (pow.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) -1) (-.f64 z y) x)
	12.1b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 7384 to 3583 computations (51.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
✓	0.8b	(pow.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) -1)
✓	1.8b	(fma.f64 (pow.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) -1) (-.f64 z y) x)

series81.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

59.0ms	(fma.f64 (pow.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) -1) (-.f64 z y) x)
22.0ms	(pow.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) -1)

rewrite72.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

918×	`prod-diff_binary64`
159×	`add-sqr-sqrt_binary64`
152×	`log1p-expm1-u_binary64`
152×	`expm1-log1p-u_binary64`
151×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	311	27
2	4324	27

Stop Event

1×	node limit

Counts

2 → 68

Calls

2 calls:

70.0ms	(pow.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) -1)
70.0ms	(fma.f64 (pow.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) -1) (-.f64 z y) x)

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

606×	`cancel-sign-sub-inv_binary64`
371×	`times-frac_binary64`
364×	`sub-neg_binary64`
318×	`associate-+r+_binary64`
274×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	3925
1	965	3921
2	3999	3906

Stop Event

1×	node limit

Counts

164 → 146

prune164.0ms (3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	191	4	195

Error

Counts

195 → 4

Alt Table

Status	Error	Program
✓	2.2b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	1.8b	(fma.f64 (*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))) (-.f64 z y) x)
✓	2.2b	(fma.f64 (pow.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) -1) (-.f64 z y) x)
	12.1b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 5206 to 2606 computations (49.9% saved)

regimes1.1s (19.9%)

Accuracy

Total 0.2b remaining (91.1%)

Threshold costs 0.2b (91.1%)

Counts

149 → 1

Compiler

Compiled 20148 to 13526 computations (32.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`*-commutative_binary64`
7×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	28	19
2	49	19
3	62	19
4	84	19
5	99	19
6	100	19

Stop Event

1×

saturated

end71.0ms (1.3%)

Compiler: Compiled 118 to 79 computations (33.1% saved)

Details

analyze1.4s (26%)

sample1.2s (21.2%)

simplify25.0ms (0.5%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series69.0ms (1.3%)

rewrite59.0ms (1.1%)

simplify79.0ms (1.5%)

prune137.0ms (2.5%)

localize9.0ms (0.2%)

series80.0ms (1.5%)

rewrite63.0ms (1.2%)

simplify87.0ms (1.6%)

prune167.0ms (3.1%)

localize8.0ms (0.2%)

series120.0ms (2.2%)

rewrite82.0ms (1.5%)

simplify70.0ms (1.3%)

prune240.0ms (4.4%)

localize9.0ms (0.2%)

series81.0ms (1.5%)

rewrite72.0ms (1.3%)

simplify80.0ms (1.5%)

prune164.0ms (3%)

regimes1.1s (19.9%)

simplify3.0ms (0.1%)

end71.0ms (1.3%)

Profiling