Details

analyze1.9s (7%)

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
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
12.9%	79.1%	8%	12
15.8%	76.2%	8%	13
18.4%	73.6%	8%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample9.7s (35.6%)

Results

3.1s	1581×	body	8192	exit
2.3s	1844×	body	1024	valid
1.4s	3922×	body	128	valid
972.0ms	1358×	body	512	valid
544.0ms	315×	body	2048	valid
459.0ms	817×	body	256	valid
338.0ms	1678×	body	128	invalid
197.0ms	222×	body	1024	invalid
151.0ms	274×	body	512	invalid
65.0ms	182×	body	256	invalid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify254.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

3540×	`fma-neg_binary64`
744×	`div-sub_binary64`
658×	`sub-neg_binary64`
627×	`fma-def_binary64`
613×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	23	18
2	48	17
3	86	17
4	177	14
5	318	14
6	465	14
7	536	14
8	618	14
9	723	14
10	1083	14
11	1710	14
12	1873	14
13	2250	14
14	2803	14
15	3186	14
16	3529	14
17	3735	14
18	3809	14
19	4125	14
20	4337	14
21	3179	14
22	3171	14
23	3183	14
24	3183	14
25	4223	14
26	7145	14

prune6.0ms (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

1.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.1b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.0b	(*.f64 y (expm1.f64 z))
✓	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	3.6b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series2.3s (8.3%)

Counts

4 → 132

Calls

4 calls:

893.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
849.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
519.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
12.0ms	(*.f64 y (expm1.f64 z))

rewrite194.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

727×	`prod-diff_binary64`
575×	`fma-udef_binary64`
263×	`fma-def_binary64`
198×	`expm1-udef_binary64`
198×	`log1p-udef_binary64`

Counts

4 → 164

Calls

4 calls:

185.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
185.0ms	(*.f64 y (expm1.f64 z))
185.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
185.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	209	39
2	2701	39
3	4872	39
4	4748	39
5	4995	39
0	0	0
1	0	0

simplify191.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

480×	`sub-neg_binary64`
305×	`fma-def_binary64`
277×	`+-commutative_binary64`
275×	`associate-+r+_binary64`
236×	`associate-+l+_binary64`

Counts

296 → 269

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	3764
1	1019	3317
2	3929	3303
3	5092	3303

prune586.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	262	7	269
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	262	8	270

Error

0.0b

Counts

270 → 8

Alt Table

Status	Error	Program
▶	1.1b	(-.f64 x (pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1))
	30.2b	(-.f64 x (-.f64 (+.f64 (/.f64 (.f64 y z) t) (+.f64 (.f64 1/2 (/.f64 (.f64 y (pow.f64 z 2)) t)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 y 3) (pow.f64 z 4)) t)) (+.f64 (.f64 1/24 (/.f64 (.f64 y (pow.f64 z 4)) t)) (+.f64 (.f64 1/3 (/.f64 (.f64 (pow.f64 y 3) (pow.f64 z 3)) t)) (.f64 1/6 (/.f64 (.f64 y (pow.f64 z 3)) t))))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 z 3)) t)) (+.f64 (.f64 7/24 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 z 4)) t)) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 y 4) (pow.f64 z 4)) t)) (.f64 1/2 (/.f64 (*.f64 (pow.f64 y 2) (pow.f64 z 2)) t)))))))
	32.1b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (sqrt.f64 t))))
	15.9b	(-.f64 x (*.f64 (/.f64 y t) z))
	18.0b	x
	1.1b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	23.6b	(-.f64 x (pow.f64 (sqrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 2))
✓	1.1b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 8112 to 3325 computations (59% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (expm1.f64 z))
	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.9b	(pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1)
✓	3.2b	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

series3.3s (12%)

Counts

2 → 72

Calls

2 calls:

1.7s	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))
1.6s	(pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1)

rewrite59.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

880×	`expm1-log1p-u_binary64`
879×	`log1p-expm1-u_binary64`
213×	`prod-diff_binary64`
99×	`add-sqr-sqrt_binary64`
90×	`add-cbrt-cube_binary64`

Counts

2 → 76

Calls

2 calls:

56.0ms	(pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1)
56.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	200	22
2	2306	22
3	5775	22
0	0	0
1	0	0

simplify144.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

781×	`associate-/l*_binary64`
687×	`fma-def_binary64`
255×	`*-commutative_binary64`
234×	`+-commutative_binary64`
200×	`associate-+r+_binary64`

Counts

148 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	789	8170
1	2819	7767
2	5097	7767

prune381.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	215	9	224

Error

0.0b

Counts

224 → 9

Alt Table

Status	Error	Program
	32.1b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
▶	1.1b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
✓	1.1b	(-.f64 x (pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1))
	30.2b	(-.f64 x (-.f64 (+.f64 (/.f64 (.f64 y z) t) (+.f64 (.f64 1/2 (/.f64 (.f64 y (pow.f64 z 2)) t)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 y 3) (pow.f64 z 4)) t)) (+.f64 (.f64 1/24 (/.f64 (.f64 y (pow.f64 z 4)) t)) (+.f64 (.f64 1/3 (/.f64 (.f64 (pow.f64 y 3) (pow.f64 z 3)) t)) (.f64 1/6 (/.f64 (.f64 y (pow.f64 z 3)) t))))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 z 3)) t)) (+.f64 (.f64 7/24 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 z 4)) t)) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 y 4) (pow.f64 z 4)) t)) (.f64 1/2 (/.f64 (*.f64 (pow.f64 y 2) (pow.f64 z 2)) t)))))))
	18.0b	x
	25.1b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
	23.6b	(-.f64 x (pow.f64 (sqrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 2))
	15.9b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	1.1b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 14047 to 8391 computations (40.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
✓	0.2b	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))
	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	3.6b	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)

series1.9s (6.9%)

Counts

3 → 84

Calls

3 calls:

902.0ms	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)
685.0ms	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
306.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))

rewrite59.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

807×	`expm1-log1p-u_binary64`
805×	`log1p-expm1-u_binary64`
248×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
81×	`pow1_binary64`

Counts

3 → 69

Calls

3 calls:

57.0ms	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
57.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))
57.0ms	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	177	29
2	2110	29
3	5419	29
0	0	0
1	0	0

simplify122.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-def_binary64`
356×	`associate-+r+_binary64`
313×	`associate-r_binary64`
272×	`associate-+l+_binary64`
266×	`associate-l_binary64`

Counts

153 → 165

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	398	3776
1	1305	3337
2	5378	3337

prune620.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	215	8	223

Error

0.0b

Counts

223 → 8

Alt Table

Status	Error	Program
	32.1b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
✓	1.1b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
✓	1.1b	(-.f64 x (pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1))
	30.2b	(-.f64 x (-.f64 (+.f64 (/.f64 (.f64 y z) t) (+.f64 (.f64 1/2 (/.f64 (.f64 y (pow.f64 z 2)) t)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 y 3) (pow.f64 z 4)) t)) (+.f64 (.f64 1/24 (/.f64 (.f64 y (pow.f64 z 4)) t)) (+.f64 (.f64 1/3 (/.f64 (.f64 (pow.f64 y 3) (pow.f64 z 3)) t)) (.f64 1/6 (/.f64 (.f64 y (pow.f64 z 3)) t))))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 z 3)) t)) (+.f64 (.f64 7/24 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 z 4)) t)) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 y 4) (pow.f64 z 4)) t)) (.f64 1/2 (/.f64 (*.f64 (pow.f64 y 2) (pow.f64 z 2)) t)))))))
	18.0b	x
▶	13.6b	(-.f64 x (-.f64 (/.f64 (+.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 1) t) (/.f64 1 t)))
	23.6b	(-.f64 x (pow.f64 (sqrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 2))
	15.9b	(-.f64 x (*.f64 (/.f64 y t) z))

Compiler

Compiled 7584 to 4385 computations (42.2% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (expm1.f64 z))
✓	0.1b	(/.f64 (+.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 1) t)
	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	3.0b	(-.f64 (/.f64 (+.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 1) t) (/.f64 1 t))

series3.1s (11.5%)

Counts

2 → 72

Calls

2 calls:

1.6s	(/.f64 (+.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 1) t)
1.5s	(-.f64 (/.f64 (+.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 1) t) (/.f64 1 t))

rewrite154.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

427×	`fma-def_binary64`
273×	`fma-neg_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
169×	`egg-rr`

Counts

2 → 169

Calls

2 calls:

147.0ms	(/.f64 (+.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 1) t)
147.0ms	(-.f64 (/.f64 (+.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 1) t) (/.f64 1 t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	263	25
2	3453	25
3	5000	25
4	4987	25
0	0	0
1	0	0

simplify158.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

431×	`fma-def_binary64`
355×	`associate-/l*_binary64`
255×	`sub-neg_binary64`
217×	`fma-neg_binary64`
188×	`cancel-sign-sub-inv_binary64`

Counts

241 → 233

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	221	2561
1	677	2241
2	2361	2095
3	4945	2091
4	5092	2091

prune735.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	306	1	307
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	308	7	315

Error

0.0b

Counts

315 → 7

Alt Table

Status	Error	Program
	32.1b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
✓	1.1b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	18.0b	x
✓	13.6b	(-.f64 x (-.f64 (/.f64 (+.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 1) t) (/.f64 1 t)))
✓	1.1b	(-.f64 x (pow.f64 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))) -1))
	23.6b	(-.f64 x (pow.f64 (sqrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) 2))
	30.5b	(-.f64 x (-.f64 (fma.f64 (/.f64 y t) z (fma.f64 1/2 (fma.f64 (/.f64 y t) (.f64 z z) (.f64 (/.f64 (pow.f64 y 3) t) (pow.f64 z 4))) (fma.f64 1/24 (.f64 (/.f64 y t) (pow.f64 z 4)) (fma.f64 1/3 (.f64 (/.f64 (pow.f64 y 3) t) (pow.f64 z 3)) (.f64 1/6 (.f64 (/.f64 y t) (pow.f64 z 3))))))) (+.f64 (fma.f64 1/4 (.f64 (/.f64 (pow.f64 y 4) t) (pow.f64 z 4)) (.f64 7/24 (.f64 (.f64 (/.f64 y t) y) (pow.f64 z 4)))) (.f64 1/2 (.f64 (.f64 (/.f64 y t) y) (+.f64 (.f64 z z) (pow.f64 z 3)))))))

Compiler

Compiled 9009 to 4925 computations (45.3% saved)

regimes1.1s (4.1%)

Accuracy

Total 1.0b remaining (86.1%)

Threshold costs 1.0b (86.1%)

Counts

66 → 1

Compiler

Compiled 12761 to 8549 computations (33% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	22	14
2	28	14
3	31	14
4	34	14
5	35	14
6	33	14

end286.0ms (1%)

Compiler: Compiled 210 to 138 computations (34.3% saved)

Details

analyze1.9s (7%)

sample9.7s (35.6%)

simplify254.0ms (0.9%)

prune6.0ms (0%)

localize7.0ms (0%)

series2.3s (8.3%)

rewrite194.0ms (0.7%)

simplify191.0ms (0.7%)

prune586.0ms (2.1%)

localize18.0ms (0.1%)

series3.3s (12%)

rewrite59.0ms (0.2%)

simplify144.0ms (0.5%)

prune381.0ms (1.4%)

localize14.0ms (0.1%)

series1.9s (6.9%)

rewrite59.0ms (0.2%)

simplify122.0ms (0.4%)

prune620.0ms (2.3%)

localize27.0ms (0.1%)

series3.1s (11.5%)

rewrite154.0ms (0.6%)

simplify158.0ms (0.6%)

prune735.0ms (2.7%)

regimes1.1s (4.1%)

simplify5.0ms (0%)

end286.0ms (1%)

Profiling