Details

analyze1.2s (8.1%)

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)

sample5.3s (35.6%)

Results

3.2s	16323×	body	128	invalid
1.5s	7618×	body	128	valid
154.0ms	278×	body	512	valid
100.0ms	117×	body	1024	valid
85.0ms	243×	body	256	valid
81.0ms	151×	body	512	invalid
49.0ms	134×	body	256	invalid
48.0ms	41×	body	1024	invalid

Compiler

Compiled 50 to 36 computations (28% saved)

preprocess36.0ms (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)

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

0.5b

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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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))
✓	0.3b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
✓	0.3b	(fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (*.f64 y (-.f64 (log.f64 z) t)))

series910.0ms (6.2%)

Counts

4 → 228

Calls

57 calls:

139.0ms	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))	x	0
106.0ms	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))	x	inf
103.0ms	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))	x	-inf
59.0ms	(*.f64 y (-.f64 (log.f64 z) t))	y	0
47.0ms	(*.f64 y (-.f64 (log.f64 z) t))	y	-inf

rewrite64.0ms (0.4%)

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

simplify126.0ms (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	10415
1	1887	9555

Stop Event

1×	node limit

Counts

310 → 248

prune288.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	244	4	248
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	244	5	249

Error

0.3b

Counts

249 → 5

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)))))
	13.0b	(pow.f64 (sqrt.f64 (.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))) 2)
	18.6b	(-.f64 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 y t))) x) (.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 y t))) (.f64 a (.f64 b x))))
▶	10.4b	(.f64 x (-.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 a b))) (.f64 y (.f64 t (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (*.f64 a b)))))))
	12.9b	(-.f64 (.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b))))) (.f64 z (.f64 (.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b))))) a)))

Compiler

Compiled 12084 to 4890 computations (59.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (*.f64 a b))
✓	0.0b	(.f64 x (-.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 a b))) (.f64 y (.f64 t (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (*.f64 a b)))))))
✓	0.3b	(*.f64 (log.f64 z) y)
✓	4.4b	(log.f64 (-.f64 1 z))

series1.4s (9.4%)

Counts

4 → 105

Calls

39 calls:

280.0ms	(.f64 x (-.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 a b))) (.f64 y (.f64 t (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (*.f64 a b)))))))	x	0
216.0ms	(.f64 x (-.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 a b))) (.f64 y (.f64 t (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (*.f64 a b)))))))	x	inf
214.0ms	(.f64 x (-.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 a b))) (.f64 y (.f64 t (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (*.f64 a b)))))))	x	-inf
59.0ms	(*.f64 (log.f64 z) y)	y	0
54.0ms	(.f64 x (-.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 a b))) (.f64 y (.f64 t (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (*.f64 a b)))))))	t	0

rewrite45.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

231×	`add-sqr-sqrt_binary64`
218×	`add-cbrt-cube_binary64`
218×	`log1p-expm1-u_binary64`
218×	`expm1-log1p-u_binary64`
214×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	90
1	453	84

Stop Event

1×	node limit

Counts

4 → 92

simplify100.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

688×	`associate-l_binary64`
678×	`fma-def_binary64`
299×	`times-frac_binary64`
271×	`*-commutative_binary64`
192×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	559	7810
1	2009	7193

Stop Event

1×	node limit

Counts

197 → 211

prune490.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	347	2	349
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	347	7	354

Error

0.2b

Counts

354 → 7

Alt Table

Status	Error	Program
▶	12.9b	(-.f64 (.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b))))) (.f64 z (.f64 (.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b))))) a)))
	39.6b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (-.f64 (/.f64 (.f64 (pow.f64 (-.f64 1 z) a) (pow.f64 z y)) (pow.f64 (exp.f64 a) b)) (.f64 y (.f64 (/.f64 (*.f64 (pow.f64 (-.f64 1 z) a) (pow.f64 z y)) (pow.f64 (exp.f64 a) b)) t))) 3)))
	25.0b	(-.f64 (fma.f64 y (.f64 a (.f64 (.f64 x (/.f64 (pow.f64 z y) (pow.f64 (exp.f64 a) b))) (.f64 z t))) (.f64 x (/.f64 (pow.f64 z y) (pow.f64 (exp.f64 a) b)))) (.f64 (.f64 x (/.f64 (pow.f64 z y) (pow.f64 (exp.f64 a) b))) (+.f64 (.f64 z a) (*.f64 y t))))
✓	0.5b	(.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b) (.f64 y (-.f64 (log.f64 z) t)))))
	13.0b	(pow.f64 (sqrt.f64 (.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))) 2)
	18.6b	(-.f64 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 y t))) x) (.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 y t))) (.f64 a (.f64 b x))))
✓	10.4b	(.f64 x (-.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 a b))) (.f64 y (.f64 t (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (*.f64 a b)))))))

Compiler

Compiled 20721 to 9248 computations (55.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b)))))
✓	0.3b	(/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (*.f64 a b))))
✓	0.3b	(.f64 z (.f64 (.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b))))) a))
✓	0.5b	(fma.f64 y t (*.f64 a b))

series2.1s (14.4%)

Counts

4 → 252

Calls

63 calls:

630.0ms	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b)))))	a	-inf
74.0ms	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b)))))	x	0
68.0ms	(.f64 z (.f64 (.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b))))) a))	x	0
62.0ms	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b)))))	x	inf
56.0ms	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b)))))	x	-inf

rewrite63.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

286×	`log1p-udef_binary64`
256×	`prod-diff_binary64`
161×	`associate-r_binary64`
159×	`add-sqr-sqrt_binary64`
146×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	68
1	308	68
2	4064	68

Stop Event

1×	node limit

Counts

4 → 98

simplify122.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

641×	`associate-r_binary64`
476×	`fma-def_binary64`
432×	`associate-l_binary64`
280×	`*-commutative_binary64`
279×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	366	7120
1	1200	7042
2	4699	7001

Stop Event

1×	node limit

Counts

350 → 197

prune422.0ms (2.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	344	1	345
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	347	5	352

Error

0.2b

Counts

352 → 5

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)))))
	13.0b	(pow.f64 (sqrt.f64 (.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))) 2)
	18.6b	(-.f64 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 y t))) x) (.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 y t))) (.f64 a (.f64 b x))))
✓	10.4b	(.f64 x (-.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 a b))) (.f64 y (.f64 t (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (*.f64 a b)))))))
▶	12.9b	(-.f64 (/.f64 x (/.f64 (exp.f64 (fma.f64 y t (.f64 a b))) (pow.f64 z y))) (.f64 z (.f64 (.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (*.f64 a b))))) a)))

Compiler

Compiled 16431 to 3316 computations (79.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b)))))
	0.3b	(/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (*.f64 a b))))
	0.3b	(.f64 z (.f64 (.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (.f64 a b))))) a))
	0.5b	(fma.f64 y t (*.f64 a b))

prune276.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	226	5	231

Error

0.2b

Counts

231 → 5

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)))))
	13.0b	(pow.f64 (sqrt.f64 (.f64 x (exp.f64 (fma.f64 a (-.f64 (log1p.f64 z) b) (.f64 y (-.f64 (log.f64 z) t)))))) 2)
	18.6b	(-.f64 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 y t))) x) (.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 y t))) (.f64 a (.f64 b x))))
✓	10.4b	(.f64 x (-.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (.f64 a b))) (.f64 y (.f64 t (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 a (log.f64 (-.f64 1 z)))) (*.f64 a b)))))))
✓	12.9b	(-.f64 (/.f64 x (/.f64 (exp.f64 (fma.f64 y t (.f64 a b))) (pow.f64 z y))) (.f64 z (.f64 (.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 y t (*.f64 a b))))) a)))

Compiler

Compiled 10711 to 2444 computations (77.2% saved)

regimes1.7s (11.3%)

Accuracy

Total 0.2b remaining (86.6%)

Threshold costs 0.2b (86.6%)

Counts

156 → 1

Compiler

Compiled 47144 to 28527 computations (39.5% saved)

simplify3.0ms (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

end103.0ms (0.7%)

Stop Event

1×

fuel

Compiler

Compiled 219 to 134 computations (38.8% saved)

Details

analyze1.2s (8.1%)

sample5.3s (35.6%)

preprocess36.0ms (0.2%)

simplify27.0ms (0.2%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series910.0ms (6.2%)

rewrite64.0ms (0.4%)

simplify126.0ms (0.9%)

prune288.0ms (1.9%)

localize18.0ms (0.1%)

series1.4s (9.4%)

rewrite45.0ms (0.3%)

simplify100.0ms (0.7%)

prune490.0ms (3.3%)

localize13.0ms (0.1%)

series2.1s (14.4%)

rewrite63.0ms (0.4%)

simplify122.0ms (0.8%)

prune422.0ms (2.9%)

localize17.0ms (0.1%)

prune276.0ms (1.9%)

regimes1.7s (11.3%)

simplify3.0ms (0%)

end103.0ms (0.7%)

Profiling