Details

analyze1.1s (5.2%)

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%	97.4%	2.6%	9
0%	47.5%	52.5%	10
0%	47.5%	52.5%	11
0%	47.5%	52.5%	12
0%	46.9%	53.1%	13
0%	46.4%	53.6%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample5.8s (26.7%)

Results

3.4s	17583×	body	128	invalid
1.8s	7605×	body	128	valid
159.0ms	291×	body	512	valid
121.0ms	133×	body	1024	valid
96.0ms	152×	body	512	invalid
82.0ms	227×	body	256	valid
40.0ms	108×	body	256	invalid
34.0ms	41×	body	1024	invalid

Compiler

Compiled 50 to 36 computations (28% saved)

preprocess39.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

580×	`fma-def_binary64`
350×	`associate-r_binary64`
332×	`associate-l_binary64`
220×	`exp-sum_binary64`
182×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	120	416
1	270	400
2	647	400
3	1803	400
0	6	6

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify26.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

456×	`unswap-sqr_binary64`
361×	`fma-def_binary64`
317×	`*-commutative_binary64`
176×	`associate-l_binary64`
175×	`exp-sum_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	34	25
2	73	25
3	180	25
4	472	25
5	1548	25
6	3802	25

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))

Compiler

Compiled 84 to 53 computations (36.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
✓	0.0b	(-.f64 (log.f64 z) t)
✓	0.1b	(*.f64 y (-.f64 (log.f64 z) t))
✓	0.5b	(fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (*.f64 y (-.f64 (log.f64 z) t)))

series957.0ms (4.4%)

Counts

4 → 179

Calls

48 calls:

138.0ms	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))	x	0
115.0ms	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))	x	inf
104.0ms	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))	x	-inf
72.0ms	(*.f64 y (-.f64 (log.f64 z) t))	y	0
48.0ms	(*.f64 y (-.f64 (log.f64 z) t))	y	inf

rewrite62.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

295×	`expm1-udef_binary64`
295×	`log1p-udef_binary64`
172×	`add-sqr-sqrt_binary64`
163×	`expm1-log1p-u_binary64`
162×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	60
1	332	56
2	4415	56

Stop Event

1×	node limit

Counts

4 → 99

simplify85.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

577×	`associate-r_binary64`
411×	`fma-def_binary64`
404×	`associate-l_binary64`
240×	`associate-+r+_binary64`
181×	`associate-+l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	354	6616
1	1285	6033

Stop Event

1×	node limit

Counts

278 → 214

prune204.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	211	4	215

Error

0.0b

Counts

215 → 4

Alt Table

Status	Error	Program
▶	3.0b	(.f64 x (exp.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t)))))))))
	8.7b	(.f64 x (exp.f64 (fma.f64 (log.f64 z) y (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.5b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
	11.5b	(/.f64 (.f64 (pow.f64 z y) x) (exp.f64 (fma.f64 y t (.f64 a b))))

Compiler

Compiled 8113 to 3251 computations (59.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (log.f64 z) t)
	0.1b	(*.f64 y (-.f64 (log.f64 z) t))
✓	0.5b	(fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t)))
✓	4.2b	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t))))))

series9.5s (43.5%)

Counts

2 → 120

Calls

30 calls:

4.0s	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t))))))	a	0
3.9s	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t))))))	y	0
197.0ms	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t))))))	b	0
191.0ms	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t))))))	t	0
129.0ms	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t))))))	y	-inf

rewrite54.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

929×	`prod-diff_binary64`
156×	`add-sqr-sqrt_binary64`
149×	`expm1-log1p-u_binary64`
148×	`log1p-expm1-u_binary64`
146×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	42
1	307	39
2	4010	39

Stop Event

1×	node limit

Counts

2 → 46

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-def_binary64`
696×	`associate--r+_binary64`
325×	`associate--l+_binary64`
241×	`cancel-sign-sub-inv_binary64`
226×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	3190
1	531	3035
2	1705	2797

Stop Event

1×	node limit

Counts

166 → 131

prune463.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	400	0	400
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	400	4	404

Error

0.0b

Counts

404 → 4

Alt Table

Status	Error	Program
✓	3.0b	(.f64 x (exp.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t)))))))))
▶	8.7b	(.f64 x (exp.f64 (fma.f64 (log.f64 z) y (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.5b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
	11.5b	(/.f64 (.f64 (pow.f64 z y) x) (exp.f64 (fma.f64 y t (.f64 a b))))

Compiler

Compiled 16532 to 4541 computations (72.5% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (exp.f64 (fma.f64 (log.f64 z) y (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.1b	(fma.f64 (log.f64 z) y (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series860.0ms (4%)

Counts

3 → 144

Calls

36 calls:

136.0ms	(.f64 x (exp.f64 (fma.f64 (log.f64 z) y (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))	x	0
126.0ms	(.f64 x (exp.f64 (fma.f64 (log.f64 z) y (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))	x	-inf
105.0ms	(.f64 x (exp.f64 (fma.f64 (log.f64 z) y (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))	x	inf
94.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))	a	0
56.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))	a	-inf

rewrite53.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

639×	`prod-diff_binary64`
245×	`log1p-udef_binary64`
145×	`add-sqr-sqrt_binary64`
136×	`expm1-log1p-u_binary64`
135×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	50
1	282	44
2	3612	44

Stop Event

1×	node limit

Counts

3 → 62

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

411×	`associate-r_binary64`
375×	`fma-neg_binary64`
357×	`fma-def_binary64`
280×	`associate-l_binary64`
242×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	302	4763
1	1080	4293
2	4463	4250

Stop Event

1×	node limit

Counts

206 → 172

prune157.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	172	4	176

Error

0.0b

Counts

176 → 4

Alt Table

Status	Error	Program
✓	3.0b	(.f64 x (exp.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t)))))))))
✓	8.7b	(.f64 x (exp.f64 (fma.f64 (log.f64 z) y (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.5b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
▶	11.5b	(/.f64 (.f64 (pow.f64 z y) x) (exp.f64 (fma.f64 y t (.f64 a b))))

Compiler

Compiled 5803 to 2660 computations (54.2% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 z y) x)
✓	0.0b	(/.f64 (.f64 (pow.f64 z y) x) (exp.f64 (fma.f64 y t (.f64 a b))))
✓	0.0b	(exp.f64 (fma.f64 y t (*.f64 a b)))
✓	0.2b	(fma.f64 y t (*.f64 a b))

series827.0ms (3.8%)

Counts

4 → 172

Calls

51 calls:

74.0ms	(/.f64 (.f64 (pow.f64 z y) x) (exp.f64 (fma.f64 y t (.f64 a b))))	x	0
63.0ms	(*.f64 (pow.f64 z y) x)	x	0
59.0ms	(/.f64 (.f64 (pow.f64 z y) x) (exp.f64 (fma.f64 y t (.f64 a b))))	x	-inf
57.0ms	(/.f64 (.f64 (pow.f64 z y) x) (exp.f64 (fma.f64 y t (.f64 a b))))	x	inf
57.0ms	(/.f64 (.f64 (pow.f64 z y) x) (exp.f64 (fma.f64 y t (.f64 a b))))	b	inf

rewrite58.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

246×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
238×	`log-pow_binary64`
221×	`prod-diff_binary64`
137×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	264	44
2	3461	44

Stop Event

1×	node limit

Counts

4 → 110

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

571×	`times-frac_binary64`
545×	`associate-/l*_binary64`
500×	`fma-def_binary64`
235×	`associate-r_binary64`
180×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	3275
1	536	3243
2	1933	3162

Stop Event

1×	node limit

Counts

282 → 169

prune164.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	169	4	173

Error

Counts

173 → 4

Alt Table

Status	Error	Program
✓	8.7b	(.f64 x (exp.f64 (fma.f64 (log.f64 z) y (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.5b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
	45.3b	(+.f64 (fma.f64 1/2 (.f64 (/.f64 (pow.f64 (log.f64 z) 2) (pow.f64 (exp.f64 b) a)) (.f64 y (.f64 y x))) (/.f64 x (pow.f64 (exp.f64 b) a))) (-.f64 (fma.f64 1/6 (.f64 (/.f64 (pow.f64 (log.f64 z) 3) (pow.f64 (exp.f64 b) a)) (.f64 (pow.f64 y 3) x)) (fma.f64 1/2 (fma.f64 (/.f64 (log.f64 z) (pow.f64 (exp.f64 b) a)) (.f64 (pow.f64 y 3) (.f64 t (.f64 t x))) (.f64 (/.f64 (.f64 y y) (pow.f64 (exp.f64 b) a)) (.f64 t (.f64 t x)))) (.f64 (/.f64 (log.f64 z) (pow.f64 (exp.f64 b) a)) (.f64 y x)))) (fma.f64 1/2 (.f64 (/.f64 (pow.f64 (log.f64 z) 2) (pow.f64 (exp.f64 b) a)) (.f64 (pow.f64 y 3) (.f64 t x))) (fma.f64 1/6 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (exp.f64 b) a)) (.f64 (pow.f64 t 3) x)) (fma.f64 (/.f64 (log.f64 z) (pow.f64 (exp.f64 b) a)) (.f64 (.f64 y y) (.f64 t x)) (.f64 (/.f64 y (pow.f64 (exp.f64 b) a)) (.f64 t x)))))))
✓	11.5b	(/.f64 (.f64 (pow.f64 z y) x) (exp.f64 (fma.f64 y t (.f64 a b))))

Compiler

Compiled 4171 to 1107 computations (73.5% saved)

regimes947.0ms (4.4%)

Accuracy

Total 0.3b remaining (93.5%)

Threshold costs 0.3b (93.5%)

Counts

100 → 1

Compiler

Compiled 27776 to 16908 computations (39.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	26	25
2	34	25
3	39	25
4	41	25

Stop Event

1×

saturated

end109.0ms (0.5%)

Stop Event

1×

fuel

Compiler

Compiled 257 to 135 computations (47.5% saved)

Details

analyze1.1s (5.2%)

sample5.8s (26.7%)

preprocess39.0ms (0.2%)

simplify26.0ms (0.1%)

prune3.0ms (0%)

localize15.0ms (0.1%)

series957.0ms (4.4%)

rewrite62.0ms (0.3%)

simplify85.0ms (0.4%)

prune204.0ms (0.9%)

localize16.0ms (0.1%)

series9.5s (43.5%)

rewrite54.0ms (0.2%)

simplify68.0ms (0.3%)

prune463.0ms (2.1%)

localize11.0ms (0.1%)

series860.0ms (4%)

rewrite53.0ms (0.2%)

simplify99.0ms (0.5%)

prune157.0ms (0.7%)

localize10.0ms (0%)

series827.0ms (3.8%)

rewrite58.0ms (0.3%)

simplify68.0ms (0.3%)

prune164.0ms (0.8%)

regimes947.0ms (4.4%)

simplify2.0ms (0%)

end109.0ms (0.5%)

Profiling