Details

analyze1.7s (21.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
3.9%	95.8%	0.3%	11
7.4%	92.3%	0.3%	12
8.8%	90.9%	0.3%	13
10.2%	89.5%	0.3%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample1.4s (18.2%)

Results

1.3s	8256×	body	128	valid
41.0ms	280×	body	128	invalid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
4×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	41	21
3	51	21
4	61	21
5	65	21
6	64	21

prune4.0ms (0%)

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

14.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	19.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
▶	17.0b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

Compiler

Compiled 126 to 78 computations (38.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y z) t))
✓	3.1b	(/.f64 (*.f64 y b) t)
✓	3.6b	(/.f64 (*.f64 y z) t)
✓	14.1b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

series215.0ms (2.8%)

Counts

4 → 120

Calls

4 calls:

175.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
14.0ms	(/.f64 (*.f64 y b) t)
13.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
13.0ms	(/.f64 (*.f64 y z) t)

rewrite95.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

841×	`prod-diff_binary64`
185×	`add-sqr-sqrt_binary64`
176×	`log1p-expm1-u_binary64`
176×	`expm1-log1p-u_binary64`
171×	`add-log-exp_binary64`

Counts

4 → 141

Calls

4 calls:

92.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
92.0ms	(/.f64 (*.f64 y b) t)
92.0ms	(/.f64 (*.f64 y z) t)
92.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	360	49
2	4858	49
3	6747	49

simplify109.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
509×	`associate-/l*_binary64`
394×	`associate-/r*_binary64`
229×	`associate-r_binary64`
220×	`fma-def_binary64`

Counts

261 → 204

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	356	7643
1	1221	7254
2	5118	7254

prune268.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	194	10	204
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	196	10	206

Error

0.3b

Counts

206 → 10

Alt Table

Status	Error	Program
	19.2b	(/.f64 (+.f64 x (.f64 (/.f64 y t) z)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	17.3b	(pow.f64 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))) -1)
	18.2b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
▶	15.9b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	35.6b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (-.f64 (pow.f64 (+.f64 a 1) 2) (pow.f64 (/.f64 (.f64 y b) t) 2))) (-.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	17.3b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 (/.f64 y t) b)))
	38.0b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	38.8b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	41.9b	(/.f64 z b)
	31.7b	(/.f64 x (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

Compiler

Compiled 9771 to 4465 computations (54.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.1b	(/.f64 (*.f64 y b) t)
✓	4.6b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	6.9b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	10.7b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series219.0ms (2.8%)

Counts

3 → 152

Calls

3 calls:

103.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
95.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
20.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)

rewrite91.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

507×	`prod-diff_binary64`
183×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
169×	`add-log-exp_binary64`

Counts

3 → 107

Calls

3 calls:

88.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
88.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
88.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	54
1	356	54
2	4962	54
3	6125	54

simplify116.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

721×	`times-frac_binary64`
498×	`associate-/l*_binary64`
386×	`associate-/r*_binary64`
224×	`associate-r_binary64`
196×	`associate-l_binary64`

Counts

259 → 179

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	272	8039
1	985	7521
2	4995	7521

prune310.0ms (4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	249	4	253
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	255	8	263

Error

0.0b

Counts

263 → 8

Alt Table

Status	Error	Program
	16.2b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (.f64 (/.f64 y 1) (/.f64 b t))))))
	29.6b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	16.5b	(+.f64 (.f64 (/.f64 y t) (/.f64 z (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	38.0b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
▶	14.8b	(+.f64 (.f64 (/.f64 y 1) (/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	38.8b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	18.2b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	17.3b	(pow.f64 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))) -1)

Compiler

Compiled 10819 to 4442 computations (58.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.6b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	5.7b	(.f64 (/.f64 y 1) (/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
✓	6.1b	(/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
✓	6.9b	(.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))

series223.0ms (2.9%)

Counts

3 → 168

Calls

3 calls:

106.0ms	(.f64 (/.f64 y 1) (/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
96.0ms	(/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
21.0ms	(.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))

rewrite88.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

292×	`log1p-udef_binary64`
164×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
152×	`add-log-exp_binary64`

Counts

3 → 128

Calls

3 calls:

84.0ms	(.f64 (/.f64 y 1) (/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
84.0ms	(/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
84.0ms	(.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	57
1	325	57
2	4688	57
3	5140	57

simplify164.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

712×	`times-frac_binary64`
500×	`associate-/l*_binary64`
396×	`associate-/r*_binary64`
287×	`fma-neg_binary64`
184×	`associate-r_binary64`

Counts

296 → 217

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	283	8355
1	969	7743
2	4946	7743
3	5211	7743

prune324.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	275	2	277
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	277	8	285

Error

0.0b

Counts

285 → 8

Alt Table

Status	Error	Program
	16.2b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (.f64 (/.f64 y 1) (/.f64 b t))))))
	29.6b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	15.7b	(+.f64 (.f64 (/.f64 y 1) (.f64 (/.f64 1 t) (/.f64 z (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	16.5b	(+.f64 (.f64 (/.f64 y t) (/.f64 z (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	38.0b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
▶	14.8b	(+.f64 (/.f64 (/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))) (/.f64 1 y)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	17.3b	(pow.f64 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))) -1)
	38.8b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))

Compiler

Compiled 13238 to 5973 computations (54.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.6b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	5.7b	(/.f64 (/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))) (/.f64 1 y))
	6.1b	(/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	6.9b	(.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))

series107.0ms (1.4%)

Counts

1 → 60

Calls

1 calls:

107.0ms

(/.f64 (/.f64 z (*.f64 t (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))) (/.f64 1 y))

rewrite80.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

814×	`prod-diff_binary64`
177×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`
164×	`add-log-exp_binary64`

Counts

1 → 40

Calls

1 calls:

79.0ms

(/.f64 (/.f64 z (*.f64 t (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))) (/.f64 1 y))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	347	22
2	4920	22
3	6659	22

simplify115.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

448×	`cancel-sign-sub-inv_binary64`
435×	`times-frac_binary64`
359×	`fma-neg_binary64`
305×	`associate-/l*_binary64`
249×	`neg-mul-1_binary64`

Counts

100 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	4037
1	615	3713
2	3179	3326
3	4566	3326
4	4990	3326

prune302.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	262	8	270

Error

0.0b

Counts

270 → 8

Alt Table

Status	Error	Program
	16.2b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (.f64 (/.f64 y 1) (/.f64 b t))))))
	29.6b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	15.7b	(+.f64 (.f64 (/.f64 y 1) (.f64 (/.f64 1 t) (/.f64 z (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	16.5b	(+.f64 (.f64 (/.f64 y t) (/.f64 z (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	38.0b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
✓	14.8b	(+.f64 (/.f64 (/.f64 z (.f64 t (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))) (/.f64 1 y)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	17.3b	(pow.f64 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))) -1)
	38.8b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))

Compiler

Compiled 12617 to 5748 computations (54.4% saved)

regimes1.6s (20.4%)

Accuracy

Total 6.0b remaining (93%)

Threshold costs 0b (0%)

Counts

126 → 4

Compiler

Compiled 30661 to 19134 computations (37.6% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 23 to 15 computations (34.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	225
1	69	225
2	73	225
3	75	225
4	76	225
5	75	225

end151.0ms (2%)

Compiler: Compiled 578 to 285 computations (50.7% saved)

Details

analyze1.7s (21.8%)

sample1.4s (18.2%)

simplify7.0ms (0.1%)

prune4.0ms (0%)

localize13.0ms (0.2%)

series215.0ms (2.8%)

rewrite95.0ms (1.2%)

simplify109.0ms (1.4%)

prune268.0ms (3.5%)

localize14.0ms (0.2%)

series219.0ms (2.8%)

rewrite91.0ms (1.2%)

simplify116.0ms (1.5%)

prune310.0ms (4%)

localize13.0ms (0.2%)

series223.0ms (2.9%)

rewrite88.0ms (1.1%)

simplify164.0ms (2.1%)

prune324.0ms (4.2%)

localize13.0ms (0.2%)

series107.0ms (1.4%)

rewrite80.0ms (1%)

simplify115.0ms (1.5%)

prune302.0ms (3.9%)

regimes1.6s (20.4%)

bsearch5.0ms (0.1%)

simplify8.0ms (0.1%)

end151.0ms (2%)

Profiling