Details

analyze1.6s (12%)

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)

sample5.7s (43.7%)

Results

1.8s	1574×	body	8192	exit
1.3s	1797×	body	1024	valid
707.0ms	3991×	body	128	valid
643.0ms	1419×	body	512	valid
372.0ms	301×	body	2048	valid
268.0ms	1665×	body	128	invalid
237.0ms	748×	body	256	valid
131.0ms	211×	body	1024	invalid
83.0ms	241×	body	512	invalid
80.0ms	167×	body	256	invalid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify45.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
369×	`fma-neg_binary64`
355×	`div-sub_binary64`
287×	`sub-neg_binary64`
210×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	23	18
2	48	17
3	96	17
4	206	14
5	423	14
6	722	14
7	906	14
8	1020	14
9	1231	14
10	1745	14
11	3240	14
12	4174	14
13	4800	14

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

1.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.5b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series794.0ms (6%)

Counts

3 → 84

Calls

3 calls:

566.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
221.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
6.0ms	(*.f64 y (expm1.f64 z))

rewrite46.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

732×	`expm1-log1p-u_binary64`
731×	`log1p-expm1-u_binary64`
213×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
73×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	159	25
2	1999	25

Stop Event

1×	node limit

Counts

3 → 64

Calls

3 calls:

45.0ms	(*.f64 y (expm1.f64 z))
45.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
45.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

525×	`cancel-sign-sub-inv_binary64`
346×	`sub-neg_binary64`
268×	`fma-def_binary64`
226×	`associate-+r+_binary64`
216×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	2462
1	879	2190
2	3455	2184

Stop Event

1×	node limit

Counts

148 → 137

prune121.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Error

0.2b

Counts

138 → 6

Alt Table

Status	Error	Program
	7.3b	(-.f64 x (/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t))
	18.6b	(-.f64 x (*.f64 (/.f64 y t) z))
▶	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	17.5b	(-.f64 x (/.f64 (pow.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) 2) t))
✓	1.5b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	17.5b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 1 t))))

Compiler

Compiled 3878 to 2081 computations (46.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series554.0ms (4.2%)

Counts

1 → 36

Calls

1 calls:

554.0ms

(*.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (/.f64 1 t))

rewrite39.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`expm1-log1p-u_binary64`
800×	`log1p-expm1-u_binary64`
204×	`prod-diff_binary64`
94×	`add-sqr-sqrt_binary64`
85×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	195	11
2	2294	11

Stop Event

1×	node limit

Counts

1 → 26

Calls

1 calls:

39.0ms

(*.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (/.f64 1 t))

simplify45.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

490×	`associate-/r*_binary64`
385×	`fma-def_binary64`
354×	`associate-/l*_binary64`
177×	`sub-neg_binary64`
168×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	1375
1	583	1215
2	2097	1128

Stop Event

1×	node limit

Counts

62 → 59

prune130.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	129	6	135

Error

0.2b

Counts

135 → 6

Alt Table

Status	Error	Program
▶	7.3b	(-.f64 x (/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t))
	18.6b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	17.5b	(-.f64 x (/.f64 (pow.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) 2) t))
✓	1.5b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	17.5b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 1 t))))

Compiler

Compiled 3780 to 2158 computations (42.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)
	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	3.0b	(/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t)
✓	24.8b	(cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3))

series1.0s (7.7%)

Counts

3 → 84

Calls

3 calls:

553.0ms	(/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t)
242.0ms	(pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)
219.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3))

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

900×	`expm1-log1p-u_binary64`
899×	`log1p-expm1-u_binary64`
219×	`prod-diff_binary64`
99×	`add-sqr-sqrt_binary64`
92×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	220	30
2	2500	30

Stop Event

1×	node limit

Counts

3 → 75

Calls

3 calls:

51.0ms	(pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)
51.0ms	(/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t)
51.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3))

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-def_binary64`
354×	`associate-r_binary64`
269×	`associate-/r*_binary64`
266×	`associate-l_binary64`
199×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	532	4931
1	1888	4559

Stop Event

1×	node limit

Counts

159 → 174

prune254.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	223	6	229

Error

0.2b

Counts

229 → 6

Alt Table

Status	Error	Program
✓	7.3b	(-.f64 x (/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t))
	18.6b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	18.0b	(-.f64 x (/.f64 y (/.f64 t z)))
✓	1.5b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
▶	17.5b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 1 t))))

Compiler

Compiled 9172 to 5464 computations (40.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 1 t))
✓	0.2b	(.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 1 t)))
	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	12.1b	(sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))

series1.5s (11.5%)

Counts

3 → 80

Calls

3 calls:

666.0ms

(*.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) (/.f64 1 t))

578.0ms

(*.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) (*.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) (/.f64 1 t)))

269.0ms

(sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))

rewrite55.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`log-prod_binary64`
207×	`prod-diff_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
189×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	236	34
2	2791	34

Stop Event

1×	node limit

Counts

3 → 78

Calls

3 calls:

54.0ms

(*.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) (/.f64 1 t))

54.0ms

(*.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) (*.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) (/.f64 1 t)))

54.0ms

(sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

464×	`cancel-sign-sub-inv_binary64`
278×	`sub-neg_binary64`
242×	`fma-def_binary64`
184×	`associate-r_binary64`
183×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	3925
1	988	3239
2	3835	3233

Stop Event

1×	node limit

Counts

158 → 148

prune270.0ms (2.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	292	6	298

Error

0.2b

Counts

298 → 6

Alt Table

Status	Error	Program
✓	7.3b	(-.f64 x (/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t))
	18.6b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	18.0b	(-.f64 x (/.f64 y (/.f64 t z)))
✓	1.5b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	17.5b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 1 t))))

Compiler

Compiled 11971 to 6285 computations (47.5% saved)

regimes431.0ms (3.3%)

Accuracy

Total 1.2b remaining (88%)

Threshold costs 0b (0%)

Counts

37 → 3

Compiler

Compiled 5872 to 3978 computations (32.3% saved)

bsearch117.0ms (0.9%)

Steps

Iters	Range		Point
2	1.4384242578785386e-195	3.64309440779076e-192	1.0409400238575313e-194
9	-1.0085804067603781e-189	-3.614597988048605e-196	-6.255462246592998e-193

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	50
1	25	50
2	37	50
3	45	50
4	51	50
5	53	50

Stop Event

1×

saturated

end91.0ms (0.7%)

Compiler: Compiled 163 to 95 computations (41.7% saved)

Details

analyze1.6s (12%)

sample5.7s (43.7%)

simplify45.0ms (0.3%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series794.0ms (6%)

rewrite46.0ms (0.4%)

simplify55.0ms (0.4%)

prune121.0ms (0.9%)

localize8.0ms (0.1%)

series554.0ms (4.2%)

rewrite39.0ms (0.3%)

simplify45.0ms (0.3%)

prune130.0ms (1%)

localize9.0ms (0.1%)

series1.0s (7.7%)

rewrite52.0ms (0.4%)

simplify68.0ms (0.5%)

prune254.0ms (1.9%)

localize10.0ms (0.1%)

series1.5s (11.5%)

rewrite55.0ms (0.4%)

simplify80.0ms (0.6%)

prune270.0ms (2.1%)

regimes431.0ms (3.3%)

bsearch117.0ms (0.9%)

simplify4.0ms (0%)

end91.0ms (0.7%)

Profiling