Details

analyze1.1s (9.4%)

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%	90.4%	9.6%	9
0%	45.2%	54.8%	10
0%	45.2%	54.8%	11
0%	45.2%	54.8%	12
0%	45.2%	54.8%	13
0%	44.4%	55.6%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample5.2s (43%)

Results

3.1s	16521×	body	128	invalid
1.5s	7628×	body	128	valid
147.0ms	280×	body	512	valid
105.0ms	111×	body	1024	valid
79.0ms	235×	body	256	valid
69.0ms	119×	body	512	invalid
46.0ms	51×	body	1024	invalid
38.0ms	112×	body	256	invalid
3.0ms	2×	body	2048	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify27.0ms (0.2%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series888.0ms (7.4%)

Counts

4 → 228

Calls

4 calls:

399.0ms	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
250.0ms	(fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (*.f64 y (-.f64 (log.f64 z) t)))
205.0ms	(*.f64 y (-.f64 (log.f64 z) t))
34.0ms	(exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (*.f64 y (-.f64 (log.f64 z) t))))

rewrite60.0ms (0.5%)

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	76
1	332	70
2	4415	70

Stop Event

1×	node limit

Counts

4 → 82

Calls

4 calls:

58.0ms	(fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (*.f64 y (-.f64 (log.f64 z) t)))
58.0ms	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
58.0ms	(exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (*.f64 y (-.f64 (log.f64 z) t))))
58.0ms	(*.f64 y (-.f64 (log.f64 z) t))

simplify108.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-def_binary64`
629×	`associate-l_binary64`
249×	`*-commutative_binary64`
174×	`times-frac_binary64`
169×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	535	10334
1	1884	9555

Stop Event

1×	node limit

Counts

310 → 245

prune221.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	243	2	245
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	243	3	246

Error

0.0b

Counts

246 → 3

Alt Table

Status	Error	Program
	15.0b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 t y (.f64 a b)))))
✓	0.1b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
▶	4.2b	(.f64 x (log.f64 (exp.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))))

Compiler

Compiled 11856 to 4788 computations (59.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series181.0ms (1.5%)

Counts

3 → 180

Calls

3 calls:

105.0ms

(exp.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t)))))

38.0ms

(exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t))))

37.0ms

(log.f64 (exp.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t))))))

rewrite57.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

929×	`prod-diff_binary64`
148×	`add-sqr-sqrt_binary64`
142×	`expm1-log1p-u_binary64`
141×	`log1p-expm1-u_binary64`
138×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	62
1	291	62
2	3800	62

Stop Event

1×	node limit

Counts

3 → 64

Calls

3 calls:

55.0ms

(log.f64 (exp.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t))))))

55.0ms

(exp.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t)))))

55.0ms

(exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (*.f64 y (-.f64 (log.f64 z) t))))

simplify161.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
355×	`*-commutative_binary64`
333×	`times-frac_binary64`
249×	`associate-r_binary64`
198×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	680	15806
1	2469	14458

Stop Event

1×	node limit

Counts

244 → 158

prune242.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	188	3	191

Error

0.0b

Counts

191 → 3

Alt Table

Status	Error	Program
▶	15.0b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 t y (.f64 a b)))))
✓	0.1b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
✓	4.2b	(.f64 x (log.f64 (exp.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))))

Compiler

Compiled 16842 to 6958 computations (58.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 z y) (exp.f64 (fma.f64 t y (*.f64 a b))))
✓	0.0b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 t y (.f64 a b)))))
✓	0.1b	(exp.f64 (fma.f64 t y (*.f64 a b)))

series936.0ms (7.8%)

Counts

3 → 148

Calls

3 calls:

556.0ms	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 t y (.f64 a b)))))
370.0ms	(/.f64 (pow.f64 z y) (exp.f64 (fma.f64 t y (*.f64 a b))))
9.0ms	(exp.f64 (fma.f64 t y (*.f64 a b)))

rewrite58.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	264	45
2	3404	45

Stop Event

1×	node limit

Counts

3 → 77

Calls

3 calls:

57.0ms	(/.f64 (pow.f64 z y) (exp.f64 (fma.f64 t y (*.f64 a b))))
57.0ms	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 t y (.f64 a b)))))
57.0ms	(exp.f64 (fma.f64 t y (*.f64 a b)))

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

861×	`times-frac_binary64`
506×	`fma-def_binary64`
293×	`associate-r_binary64`
219×	`associate-l_binary64`
162×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	4355
1	755	4283
2	2684	4190

Stop Event

1×	node limit

Counts

225 → 153

prune129.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	153	3	156

Error

0.0b

Counts

156 → 3

Alt Table

Status	Error	Program
▶	15.0b	(/.f64 1 (/.f64 (exp.f64 (fma.f64 t y (.f64 a b))) (.f64 x (pow.f64 z y))))
✓	0.1b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
✓	4.2b	(.f64 x (log.f64 (exp.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))))

Compiler

Compiled 4304 to 1184 computations (72.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (pow.f64 z y))
✓	0.0b	(/.f64 (exp.f64 (fma.f64 t y (.f64 a b))) (.f64 x (pow.f64 z y)))
✓	0.1b	(/.f64 1 (/.f64 (exp.f64 (fma.f64 t y (.f64 a b))) (.f64 x (pow.f64 z y))))
	0.1b	(exp.f64 (fma.f64 t y (*.f64 a b)))

series1.3s (10.8%)

Counts

3 → 180

Calls

3 calls:

565.0ms	(/.f64 (exp.f64 (fma.f64 t y (.f64 a b))) (.f64 x (pow.f64 z y)))
547.0ms	(/.f64 1 (/.f64 (exp.f64 (fma.f64 t y (.f64 a b))) (.f64 x (pow.f64 z y))))
185.0ms	(*.f64 x (pow.f64 z y))

rewrite58.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

272×	`expm1-udef_binary64`
272×	`log1p-udef_binary64`
221×	`prod-diff_binary64`
155×	`add-sqr-sqrt_binary64`
142×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	305	45
2	3948	45

Stop Event

1×	node limit

Counts

3 → 104

Calls

3 calls:

55.0ms	(*.f64 x (pow.f64 z y))
55.0ms	(/.f64 (exp.f64 (fma.f64 t y (.f64 a b))) (.f64 x (pow.f64 z y)))
55.0ms	(/.f64 1 (/.f64 (exp.f64 (fma.f64 t y (.f64 a b))) (.f64 x (pow.f64 z y))))

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-def_binary64`
451×	`associate-/r/_binary64`
278×	`associate-r_binary64`
216×	`associate-/l*_binary64`
207×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	225	4577
1	752	4549
2	2901	4462

Stop Event

1×	node limit

Counts

284 → 173

prune158.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	209	3	212

Error

0.0b

Counts

212 → 3

Alt Table

Status	Error	Program
✓	15.0b	(/.f64 1 (/.f64 (exp.f64 (fma.f64 t y (.f64 a b))) (.f64 x (pow.f64 z y))))
✓	0.1b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
✓	4.2b	(.f64 x (log.f64 (exp.f64 (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))))

Compiler

Compiled 5857 to 1627 computations (72.2% saved)

regimes864.0ms (7.2%)

Accuracy

Total 0.1b remaining (43.4%)

Threshold costs 0.1b (43.4%)

Counts

107 → 1

Compiler

Compiled 18902 to 13065 computations (30.9% 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

end67.0ms (0.6%)

Compiler: Compiled 110 to 75 computations (31.8% saved)

Details

analyze1.1s (9.4%)

sample5.2s (43%)

simplify27.0ms (0.2%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series888.0ms (7.4%)

rewrite60.0ms (0.5%)

simplify108.0ms (0.9%)

prune221.0ms (1.8%)

localize16.0ms (0.1%)

series181.0ms (1.5%)

rewrite57.0ms (0.5%)

simplify161.0ms (1.3%)

prune242.0ms (2%)

localize10.0ms (0.1%)

series936.0ms (7.8%)

rewrite58.0ms (0.5%)

simplify76.0ms (0.6%)

prune129.0ms (1.1%)

localize11.0ms (0.1%)

series1.3s (10.8%)

rewrite58.0ms (0.5%)

simplify85.0ms (0.7%)

prune158.0ms (1.3%)

regimes864.0ms (7.2%)

simplify2.0ms (0%)

end67.0ms (0.6%)

Profiling