Details

analyze245.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
12.5%	43.7%	43.8%	7
12.5%	43.7%	43.8%	8
25%	28.1%	47%	9
28.1%	20.3%	51.6%	10
28.1%	20.3%	51.6%	11
34.3%	13.3%	52.4%	12
35.9%	9.8%	54.4%	13
35.9%	9.8%	54.4%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample1.3s (7%)

Results

1.0s	8256×	body	128	valid
47.0ms	390×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify285.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

990×	`fma-def_binary64`
806×	`fma-neg_binary64`
746×	`unsub-neg_binary64`
520×	`distribute-rgt-in_binary64`
485×	`distribute-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	29	16
2	59	16
3	115	16
4	270	14
5	514	14
6	792	14
7	1191	14
8	1435	14
9	1716	14
10	2343	14
11	2639	14
12	2704	14
13	3251	14
14	3766	14
15	3977	14
16	4124	14
17	4234	14
18	4260	14
19	4085	14
20	4111	14
21	4149	14
22	4189	14
23	4189	14
24	4189	14
25	4871	14
26	4999	14
27	4907	14

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	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))

Compiler

Compiled 51 to 31 computations (39.2% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
✓	0.0b	(-.f64 (log.f64 z) z)
✓	0.2b	(fma.f64 y (-.f64 (log.f64 z) z) y)

series279.0ms (1.5%)

Counts

3 → 69

Calls

3 calls:

195.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
79.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
5.0ms	(-.f64 (log.f64 z) z)

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
8×	`pow1_binary64`

Counts

3 → 58

Calls

3 calls:

3.0ms	(-.f64 (log.f64 z) z)
0.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
0.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))

simplify129.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-neg_binary64`
513×	`fma-def_binary64`
353×	`associate-l_binary64`
311×	`exp-prod_binary64`
278×	`associate-r_binary64`

Counts

127 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1706
1	274	1350
2	803	1312
3	3226	1312
4	4661	1312
5	4985	1312
6	4989	1312
7	4905	1312

prune103.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	8	94

Error

0.0b

Counts

94 → 8

Alt Table

Status	Error	Program
	0.8b	(fma.f64 x 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
	16.4b	(fma.f64 y (log.f64 z) (fma.f64 1/2 x y))
	14.7b	(fma.f64 x 1/2 (fma.f64 y (/.f64 (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3)) (fma.f64 z z (*.f64 (log.f64 z) (+.f64 z (log.f64 z))))) y))
▶	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	29.6b	(fma.f64 x 1/2 (cbrt.f64 (.f64 (.f64 (fma.f64 y (-.f64 (log.f64 z) z) y) (fma.f64 y (-.f64 (log.f64 z) z) y)) (fma.f64 y (-.f64 (log.f64 z) z) y))))
	14.7b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (.f64 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)) (-.f64 (log.f64 z) z))) y))
	16.4b	(fma.f64 x 1/2 (+.f64 (*.f64 (log.f64 z) y) y))

Compiler

Compiled 1855 to 704 computations (62% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
✓	0.2b	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
✓	0.5b	(cbrt.f64 z)
✓	0.6b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))

series1.8s (9.9%)

Counts

4 → 60

Calls

4 calls:

1.5s	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
239.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
61.0ms	(cbrt.f64 z)
38.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
34×	`pow1_binary64`
33×	`add-sqr-sqrt_binary64`
25×	`associate-+r+_binary64`
25×	`add-cube-cbrt_binary64`

Counts

4 → 127

Calls

4 calls:

12.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)
0.0ms	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

669×	`distribute-rgt-in_binary64`
601×	`distribute-lft-in_binary64`
521×	`fma-neg_binary64`
322×	`cancel-sign-sub-inv_binary64`
273×	`log-prod_binary64`

Counts

187 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	2646
1	390	1654
2	1365	1572
3	4136	1562
4	5098	1562

prune262.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	222	2	224
Fresh	4	2	6
Picked	0	1	1
Done	1	0	1
Total	227	5	232

Error

0.0b

Counts

232 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
▶	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 z)))) z))))
	16.4b	(fma.f64 y (log.f64 z) (fma.f64 1/2 x y))
	16.4b	(fma.f64 x 1/2 (+.f64 (*.f64 (log.f64 z) y) y))
	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (pow.f64 (pow.f64 z 1/6) 5)) (-.f64 (log.f64 (sqrt.f64 (cbrt.f64 z))) z)) y))

Compiler

Compiled 5241 to 1824 computations (65.2% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 z)))) z)))
✓	0.3b	(fma.f64 y (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y)
✓	0.5b	(cbrt.f64 (neg.f64 z))
✓	6.0b	(pow.f64 z 2/3)

series7.7s (41.4%)

Counts

4 → 72

Calls

4 calls:

4.0s	(+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 z)))) z)))
3.6s	(fma.f64 y (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y)
66.0ms	(pow.f64 z 2/3)
38.0ms	(cbrt.f64 (neg.f64 z))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`associate-+r+_binary64`
36×	`prod-diff_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`

Counts

4 → 112

Calls

4 calls:

9.0ms	(+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 z)))) z)))
1.0ms	(pow.f64 z 2/3)
1.0ms	(cbrt.f64 (neg.f64 z))
0.0ms	(fma.f64 y (log.f64 (*.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y)

simplify167.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-def_binary64`
383×	`distribute-rgt-in_binary64`
353×	`distribute-lft-in_binary64`
322×	`log-prod_binary64`
294×	`associate-+l+_binary64`

Counts

184 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	220	4693
1	379	4427
2	1105	4140
3	4575	4140
4	5002	4140

prune277.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	167	6	173

Error

Counts

173 → 6

Alt Table

Status	Error	Program
	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (pow.f64 (pow.f64 z 1/6) 5)) (-.f64 (log.f64 (sqrt.f64 (cbrt.f64 z))) z)) y))
	0.1b	(fma.f64 x 1/2 (+.f64 (.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2)))) (fma.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 z)))) z) y)))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
▶	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 (pow.f64 z (sqrt.f64 2/3)) (sqrt.f64 2/3)) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 z)))) z))))
	0.3b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 (pow.f64 z (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3)) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 z)))) z))))
	16.4b	(fma.f64 x 1/2 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) (fma.f64 y (log.f64 (.f64 (cbrt.f64 z) (pow.f64 (cbrt.f64 -1) 2))) y)))

Compiler

Compiled 6613 to 4163 computations (37% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 y (log.f64 (*.f64 (pow.f64 (pow.f64 z (sqrt.f64 2/3)) (sqrt.f64 2/3)) (pow.f64 (cbrt.f64 -1) 2))) y)
	0.5b	(cbrt.f64 (neg.f64 z))
✓	1.9b	(pow.f64 (pow.f64 z (sqrt.f64 2/3)) (sqrt.f64 2/3))
✓	2.0b	(pow.f64 z (sqrt.f64 2/3))

series4.4s (23.4%)

Counts

3 → 48

Calls

3 calls:

4.0s	(fma.f64 y (log.f64 (*.f64 (pow.f64 (pow.f64 z (sqrt.f64 2/3)) (sqrt.f64 2/3)) (pow.f64 (cbrt.f64 -1) 2))) y)
355.0ms	(pow.f64 (pow.f64 z (sqrt.f64 2/3)) (sqrt.f64 2/3))
25.0ms	(pow.f64 z (sqrt.f64 2/3))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`unpow-prod-down_binary64`
12×	`pow-unpow_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 60

Calls

3 calls:

2.0ms	(pow.f64 (pow.f64 z (sqrt.f64 2/3)) (sqrt.f64 2/3))
2.0ms	(pow.f64 z (sqrt.f64 2/3))
0.0ms	(fma.f64 y (log.f64 (*.f64 (pow.f64 (pow.f64 z (sqrt.f64 2/3)) (sqrt.f64 2/3)) (pow.f64 (cbrt.f64 -1) 2))) y)

simplify80.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

563×	`distribute-rgt-in_binary64`
531×	`distribute-lft-in_binary64`
455×	`fma-def_binary64`
289×	`log-prod_binary64`
239×	`sqr-pow_binary64`

Counts

108 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1510
1	238	1301
2	569	1289
3	1571	1243
4	4801	1243
5	5080	1243

prune193.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	116	6	122

Error

Counts

122 → 6

Alt Table

Status	Error	Program
	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (pow.f64 (pow.f64 z 1/6) 5)) (-.f64 (log.f64 (sqrt.f64 (cbrt.f64 z))) z)) y))
	0.1b	(fma.f64 x 1/2 (+.f64 (.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2)))) (fma.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 z)))) z) y)))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
✓	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 (pow.f64 z (sqrt.f64 2/3)) (sqrt.f64 2/3)) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 z)))) z))))
	0.3b	(fma.f64 x 1/2 (+.f64 (fma.f64 y (log.f64 (.f64 (pow.f64 (pow.f64 z (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3)) (pow.f64 (cbrt.f64 -1) 2))) y) (.f64 y (-.f64 (log.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 z)))) z))))
	16.4b	(fma.f64 x 1/2 (fma.f64 y (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) (fma.f64 y (log.f64 (.f64 (cbrt.f64 z) (pow.f64 (cbrt.f64 -1) 2))) y)))

Compiler

Compiled 4347 to 3142 computations (27.7% saved)

regimes982.0ms (5.3%)

Accuracy

Total 0.1b remaining (86.4%)

Threshold costs 0.1b (86.4%)

Counts

100 → 1

Compiler

Compiled 17348 to 12036 computations (30.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	49
1	32	49
2	35	49
3	36	49
4	36	49

end181.0ms (1%)

Compiler: Compiled 240 to 184 computations (23.3% saved)

Details

analyze245.0ms (1.3%)

sample1.3s (7%)

simplify285.0ms (1.5%)

prune3.0ms (0%)

localize8.0ms (0%)

series279.0ms (1.5%)

rewrite7.0ms (0%)

simplify129.0ms (0.7%)

prune103.0ms (0.6%)

localize13.0ms (0.1%)

series1.8s (9.9%)

rewrite27.0ms (0.1%)

simplify89.0ms (0.5%)

prune262.0ms (1.4%)

localize21.0ms (0.1%)

series7.7s (41.4%)

rewrite24.0ms (0.1%)

simplify167.0ms (0.9%)

prune277.0ms (1.5%)

localize29.0ms (0.2%)

series4.4s (23.4%)

rewrite7.0ms (0%)

simplify80.0ms (0.4%)

prune193.0ms (1%)

regimes982.0ms (5.3%)

simplify3.0ms (0%)

end181.0ms (1%)

Profiling