Details

analyze235.0ms (3.1%)

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 (17.2%)

Results

1.0s	8256×	body	128	valid
52.0ms	415×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify283.0ms (3.7%)

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 (0.1%)

Local error

Found 3 expressions with local error:

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

series298.0ms (3.9%)

Counts

3 → 69

Calls

3 calls:

201.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
92.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
5.0ms	(-.f64 (log.f64 z) z)

rewrite8.0ms (0.1%)

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:

4.0ms	(-.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))

simplify125.0ms (1.6%)

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

prune67.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	5	94

Error

0.0b

Counts

94 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
▶	0.1b	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
	14.1b	(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))
	30.2b	(fma.f64 x 1/2 (*.f64 (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y)) (sqrt.f64 (fma.f64 y (-.f64 (log.f64 z) z) y))))
	0.7b	(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))))

Compiler

Compiled 1739 to 648 computations (62.7% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x)))
✓	0.3b	(*.f64 (log.f64 z) y)

series301.0ms (3.9%)

Counts

2 → 22

Calls

2 calls:

201.0ms	(*.f64 (log.f64 z) y)
99.0ms	(+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64`
4×	`associate-l_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x)))
3.0ms	(*.f64 (log.f64 z) y)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-neg_binary64`
520×	`neg-sub0_binary64`
482×	`neg-mul-1_binary64`
381×	`distribute-rgt-neg-out_binary64`
369×	`associate-l_binary64`

Counts

59 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	756
1	224	601
2	632	600
3	2636	600
4	4076	600
5	5100	600

prune64.0ms (0.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	59	6	65
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	61	9	70

Error

0.0b

Counts

70 → 9

Alt Table

Status	Error	Program
	33.1b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (log.f64 z) y)) (sqrt.f64 (.f64 (log.f64 z) y))) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
▶	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (cbrt.f64 (.f64 (log.f64 z) y))) (cbrt.f64 (.f64 (log.f64 z) y))) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
✓	0.1b	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
	14.1b	(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))
	28.1b	(-.f64 (/.f64 (-.f64 (.f64 (.f64 (log.f64 z) y) (.f64 (log.f64 z) y)) (.f64 (+.f64 y (.f64 1/2 x)) (+.f64 y (.f64 1/2 x)))) (-.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x)))) (*.f64 y z))
	37.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 (log.f64 z) y) 3) (pow.f64 (+.f64 y (.f64 1/2 x)) 3)) (+.f64 (.f64 (.f64 (log.f64 z) y) (.f64 (log.f64 z) y)) (-.f64 (.f64 (+.f64 y (.f64 1/2 x)) (+.f64 y (.f64 1/2 x))) (.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x)))))) (.f64 y z))
	0.4b	(-.f64 (+.f64 (.f64 (.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 (log.f64 z))) (.f64 (cbrt.f64 (log.f64 z)) y)) (+.f64 y (.f64 1/2 x))) (*.f64 y z))

Compiler

Compiled 1740 to 797 computations (54.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (log.f64 z) y)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (cbrt.f64 (.f64 (log.f64 z) y))) (cbrt.f64 (*.f64 (log.f64 z) y)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (cbrt.f64 (*.f64 (log.f64 z) y)))
✓	0.6b	(cbrt.f64 (*.f64 (log.f64 z) y))

series2.2s (28.8%)

Counts

3 → 72

Calls

3 calls:

1.1s

(*.f64 (cbrt.f64 (*.f64 (log.f64 z) y)) (cbrt.f64 (*.f64 (log.f64 z) y)))

833.0ms

(cbrt.f64 (*.f64 (log.f64 z) y))

273.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (log.f64 z) y)) (cbrt.f64 (*.f64 (log.f64 z) y))) (cbrt.f64 (*.f64 (log.f64 z) y)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (log.f64 z) y)) (cbrt.f64 (*.f64 (log.f64 z) y))) (cbrt.f64 (*.f64 (log.f64 z) y)))

4.0ms

(*.f64 (cbrt.f64 (*.f64 (log.f64 z) y)) (cbrt.f64 (*.f64 (log.f64 z) y)))

2.0ms

(cbrt.f64 (*.f64 (log.f64 z) y))

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

554×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
300×	`log-prod_binary64`
294×	`fma-def_binary64`
247×	`unswap-sqr_binary64`

Counts

151 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1809
1	264	1570
2	677	1394
3	1439	1271
4	4713	1271
5	4976	1271

prune266.0ms (3.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	249	8	257

Error

0.0b

Counts

257 → 8

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
▶	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 y))) (cbrt.f64 (.f64 (log.f64 z) y))) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
	33.1b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (log.f64 z) y)) (sqrt.f64 (.f64 (log.f64 z) y))) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
✓	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (cbrt.f64 (.f64 (log.f64 z) y))) (cbrt.f64 (.f64 (log.f64 z) y))) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
	14.1b	(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))
	37.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 (log.f64 z) y) 3) (pow.f64 (+.f64 y (.f64 1/2 x)) 3)) (+.f64 (.f64 (.f64 (log.f64 z) y) (.f64 (log.f64 z) y)) (-.f64 (.f64 (+.f64 y (.f64 1/2 x)) (+.f64 y (.f64 1/2 x))) (.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x)))))) (.f64 y z))
	0.4b	(-.f64 (+.f64 (.f64 (.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (+.f64 y (.f64 1/2 x))) (*.f64 y z))

Compiler

Compiled 8001 to 2431 computations (69.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series1.5s (19.4%)

Counts

3 → 48

Calls

3 calls:

1.1s	(.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (*.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 y)))
366.0ms	(cbrt.f64 (log.f64 z))
30.0ms	(cbrt.f64 y)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1/3_binary64`
9×	`cbrt-prod_binary64`
9×	`pow1_binary64`
8×	`add-exp-log_binary64`
7×	`pow-prod-down_binary64`

Counts

3 → 52

Calls

3 calls:

6.0ms	(.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (*.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 y)))
1.0ms	(cbrt.f64 (log.f64 z))
1.0ms	(cbrt.f64 y)

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Rules

540×	`distribute-rgt-in_binary64`
493×	`distribute-lft-in_binary64`
425×	`fma-def_binary64`
357×	`log-prod_binary64`
278×	`*-commutative_binary64`

Counts

100 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1154
1	244	1118
2	702	1110
3	1763	949
4	4726	949
5	5026	949

prune133.0ms (1.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	119	9	128

Error

0.0b

Counts

128 → 9

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 y))) (.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 y))) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
✓	0.1b	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
✓	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 y))) (cbrt.f64 (.f64 (log.f64 z) y))) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
	33.1b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (log.f64 z) y)) (sqrt.f64 (.f64 (log.f64 z) y))) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
✓	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 z) y)) (cbrt.f64 (.f64 (log.f64 z) y))) (cbrt.f64 (.f64 (log.f64 z) y))) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
	14.1b	(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))
	37.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 (log.f64 z) y) 3) (pow.f64 (+.f64 y (.f64 1/2 x)) 3)) (+.f64 (.f64 (.f64 (log.f64 z) y) (.f64 (log.f64 z) y)) (-.f64 (.f64 (+.f64 y (.f64 1/2 x)) (+.f64 y (.f64 1/2 x))) (.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x)))))) (.f64 y z))
	0.4b	(-.f64 (+.f64 (.f64 (.f64 (log.f64 z) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (+.f64 y (.f64 1/2 x))) (*.f64 y z))

Compiler

Compiled 4098 to 1427 computations (65.2% saved)

regimes404.0ms (5.3%)

Accuracy

Total 0.1b remaining (65.5%)

Threshold costs 0.1b (65.5%)

Counts

52 → 1

Compiler

Compiled 8392 to 4883 computations (41.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	16	17
2	26	17
3	32	17
4	36	17
5	37	17
6	37	17

end148.0ms (1.9%)

Compiler: Compiled 283 to 158 computations (44.2% saved)

Details

analyze235.0ms (3.1%)

sample1.3s (17.2%)

simplify283.0ms (3.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series298.0ms (3.9%)

rewrite8.0ms (0.1%)

simplify125.0ms (1.6%)

prune67.0ms (0.9%)

localize10.0ms (0.1%)

series301.0ms (3.9%)

rewrite8.0ms (0.1%)

simplify66.0ms (0.9%)

prune64.0ms (0.8%)

localize12.0ms (0.2%)

series2.2s (28.8%)

rewrite16.0ms (0.2%)

simplify90.0ms (1.2%)

prune266.0ms (3.5%)

localize17.0ms (0.2%)

series1.5s (19.4%)

rewrite10.0ms (0.1%)

simplify80.0ms (1%)

prune133.0ms (1.7%)

regimes404.0ms (5.3%)

simplify4.0ms (0%)

end148.0ms (1.9%)

Profiling