Details

analyze1.6s (10.6%)

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)

sample6.6s (43.6%)

Results

1.9s	1522×	body	8192	exit
1.7s	1818×	body	1024	valid
842.0ms	1377×	body	512	valid
701.0ms	3913×	body	128	valid
432.0ms	316×	body	2048	valid
335.0ms	832×	body	256	valid
236.0ms	1688×	body	128	invalid
109.0ms	198×	body	1024	invalid
97.0ms	245×	body	512	invalid
49.0ms	167×	body	256	invalid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify248.0ms (1.6%)

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

prune4.0ms (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

1.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.4b	(-.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (expm1.f64 z))
✓	0.5b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.1b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.1s (7%)

Counts

3 → 84

Calls

3 calls:

771.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
287.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
6.0ms	(*.f64 y (expm1.f64 z))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 60

Calls

3 calls:

2.0ms	(*.f64 y (expm1.f64 z))
2.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
0.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))

simplify92.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

529×	`cancel-sign-sub-inv_binary64`
350×	`sub-neg_binary64`
280×	`fma-def_binary64`
226×	`associate-+r+_binary64`
221×	`fma-neg_binary64`

Counts

144 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	352	3383
1	1001	2974
2	3746	2968
3	5386	2968

prune120.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	133	7	140
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	7	141

Error

Counts

141 → 7

Alt Table

Status	Error	Program
	17.9b	(-.f64 x (/.f64 (log1p.f64 (fma.f64 y z (.f64 1/2 (.f64 y (*.f64 z z))))) t))
	1.6b	(-.f64 x (/.f64 (log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z)))) t))
	19.4b	(-.f64 x (*.f64 (/.f64 y t) z))
	32.7b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
▶	1.5b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	18.5b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))

Compiler

Compiled 4089 to 2082 computations (49.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (expm1.f64 z))
	0.5b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.9b	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
✓	4.1b	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

series1.5s (10%)

Counts

2 → 72

Calls

2 calls:

792.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))
715.0ms	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
2.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

simplify133.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

389×	`associate-r_binary64`
291×	`associate-/r*_binary64`
278×	`associate-/l*_binary64`
265×	`times-frac_binary64`
260×	`associate-l_binary64`

Counts

179 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	501	6217
1	1447	5548
2	4978	5546
3	5092	5546

prune279.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	278	7	285

Error

Counts

285 → 7

Alt Table

Status	Error	Program
	17.9b	(-.f64 x (/.f64 (log1p.f64 (fma.f64 y z (.f64 1/2 (.f64 y (*.f64 z z))))) t))
	1.6b	(-.f64 x (/.f64 (log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z)))) t))
	19.4b	(-.f64 x (*.f64 (/.f64 y t) z))
	32.7b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
▶	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
✓	1.5b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	18.5b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))

Compiler

Compiled 9415 to 4654 computations (50.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (expm1.f64 z))
	0.5b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.2b	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))

series718.0ms (4.7%)

Counts

1 → 36

Calls

1 calls:

718.0ms

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

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 38

Calls

1 calls:

5.0ms

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

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

409×	`associate-/l*_binary64`
389×	`fma-def_binary64`
208×	`fma-neg_binary64`
180×	`sub-neg_binary64`
168×	`distribute-rgt-in_binary64`

Counts

74 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	245	2012
1	684	1753
2	2279	1666
3	4893	1664
4	5008	1664

prune152.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	163	7	170

Error

Counts

170 → 7

Alt Table

Status	Error	Program
	17.9b	(-.f64 x (/.f64 (log1p.f64 (fma.f64 y z (.f64 1/2 (.f64 y (*.f64 z z))))) t))
▶	1.6b	(-.f64 x (/.f64 (log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z)))) t))
	19.4b	(-.f64 x (*.f64 (/.f64 y t) z))
	32.7b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
✓	1.5b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	18.5b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))

Compiler

Compiled 4590 to 2438 computations (46.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))
✓	0.4b	(cbrt.f64 (expm1.f64 z))
✓	0.5b	(log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z))))
✓	4.1b	(/.f64 (log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z)))) t)

series1.5s (9.8%)

Counts

4 → 84

Calls

4 calls:

759.0ms	(/.f64 (log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z)))) t)
299.0ms	(log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z))))
244.0ms	(*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))
181.0ms	(cbrt.f64 (expm1.f64 z))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
19×	`cbrt-prod_binary64`
11×	`pow1_binary64`

Counts

4 → 95

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))
2.0ms	(/.f64 (log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z)))) t)
1.0ms	(cbrt.f64 (expm1.f64 z))
0.0ms	(log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z))))

simplify144.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

389×	`fma-neg_binary64`
351×	`sub-neg_binary64`
301×	`fma-def_binary64`
241×	`associate-+r+_binary64`
241×	`associate-r_binary64`

Counts

179 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	409	3951
1	1140	3464
2	4080	3408
3	4995	3408
4	5097	3408

prune248.0ms (1.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	276	7	283

Error

Counts

283 → 7

Alt Table

Status	Error	Program
	17.9b	(-.f64 x (/.f64 (log1p.f64 (fma.f64 y z (.f64 1/2 (.f64 y (*.f64 z z))))) t))
✓	1.6b	(-.f64 x (/.f64 (log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z)))) t))
	19.4b	(-.f64 x (*.f64 (/.f64 y t) z))
	32.7b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
✓	1.5b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	18.5b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))

Compiler

Compiled 7902 to 3219 computations (59.3% saved)

regimes482.0ms (3.2%)

Accuracy

Total 0.9b remaining (88.1%)

Threshold costs 0.9b (88.1%)

Counts

66 → 1

Compiler

Compiled 10944 to 7181 computations (34.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	18	14
2	24	14
3	28	14
4	31	14
5	32	14
6	31	14

end95.0ms (0.6%)

Compiler: Compiled 146 to 93 computations (36.3% saved)

Details

analyze1.6s (10.6%)

sample6.6s (43.6%)

simplify248.0ms (1.6%)

prune4.0ms (0%)

localize7.0ms (0%)

series1.1s (7%)

rewrite7.0ms (0%)

simplify92.0ms (0.6%)

prune120.0ms (0.8%)

localize8.0ms (0.1%)

series1.5s (10%)

rewrite15.0ms (0.1%)

simplify133.0ms (0.9%)

prune279.0ms (1.8%)

localize8.0ms (0.1%)

series718.0ms (4.7%)

rewrite7.0ms (0%)

simplify79.0ms (0.5%)

prune152.0ms (1%)

localize11.0ms (0.1%)

series1.5s (9.8%)

rewrite11.0ms (0.1%)

simplify144.0ms (0.9%)

prune248.0ms (1.6%)

regimes482.0ms (3.2%)

simplify3.0ms (0%)

end95.0ms (0.6%)

Profiling