Details

analyze257.0ms (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)

sample1.4s (16.4%)

Results

1.1s	8256×	body	128	valid
61.0ms	417×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify287.0ms (3.4%)

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	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
✓	0.0b	(-.f64 (log.f64 z) z)
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) z) y)

series321.0ms (3.8%)

Counts

3 → 69

Calls

3 calls:

218.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
97.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
6.0ms	(-.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))

simplify134.0ms (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

prune80.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	6	94

Error

0.0b

Counts

94 → 6

Alt Table

Status	Error	Program
	0.1b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	0.5b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (fma.f64 (.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 (log.f64 z))) (cbrt.f64 (log.f64 z)) (neg.f64 (.f64 (sqrt.f64 z) (sqrt.f64 z)))) (fma.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sqrt.f64 z)))) y))
	29.7b	(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))))
	0.8b	(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 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	17.9b	(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))

Compiler

Compiled 1834 to 684 computations (62.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
✓	0.1b	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series2.0s (23.2%)

Counts

4 → 60

Calls

4 calls:

1.7s	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
260.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
36.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
30.0ms	(cbrt.f64 z)

rewrite27.0ms (0.3%)

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:

13.0ms	(+.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)

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

664×	`distribute-rgt-in_binary64`
592×	`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	1359	1572
3	4136	1562
4	5098	1562

prune275.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	218	6	224
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	224	6	230

Error

0.0b

Counts

230 → 6

Alt Table

Status	Error	Program
	0.1b	(fma.f64 x 1/2 (+.f64 (*.f64 (-.f64 (log.f64 z) z) y) y))
	0.1b	(fma.f64 x 1/2 (+.f64 (.f64 y (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))) y))
	0.2b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (fma.f64 1 (log.f64 (cbrt.f64 z)) (neg.f64 (.f64 (sqrt.f64 z) (sqrt.f64 z))))) (fma.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sqrt.f64 z)))) y))
	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y))
▶	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (log.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))))) (-.f64 (log.f64 (cbrt.f64 (cbrt.f64 z))) z)) y))

Compiler

Compiled 5394 to 1895 computations (64.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
✓	0.7b	(cbrt.f64 (cbrt.f64 z))

series604.0ms (7.1%)

Counts

2 → 24

Calls

2 calls:

345.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
258.0ms	(cbrt.f64 (cbrt.f64 z))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

3.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
1.0ms	(cbrt.f64 (cbrt.f64 z))

simplify106.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

693×	`sqr-pow_binary64`
622×	`fma-def_binary64`
548×	`unswap-sqr_binary64`
376×	`distribute-rgt-in_binary64`
318×	`*-commutative_binary64`

Counts

51 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	474
1	78	474
2	138	474
3	283	468
4	779	450
5	1271	450
6	1449	450
7	1730	450
8	2156	450
9	2689	450
10	3638	450
11	4799	450
12	4840	450

prune346.0ms (4.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	250	6	256

Error

0.0b

Counts

256 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x 1/2 (+.f64 (*.f64 (-.f64 (log.f64 z) z) y) y))
	0.1b	(fma.f64 x 1/2 (+.f64 (.f64 y (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))) y))
	0.2b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (fma.f64 1 (log.f64 (cbrt.f64 z)) (neg.f64 (.f64 (sqrt.f64 z) (sqrt.f64 z))))) (fma.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sqrt.f64 z)))) y))
	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (log.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))))) (-.f64 (log.f64 (cbrt.f64 (cbrt.f64 z))) z)) y))

Compiler

Compiled 8143 to 2423 computations (70.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series518.0ms (6.1%)

Counts

3 → 84

Calls

3 calls:

212.0ms	(+.f64 (*.f64 (-.f64 (log.f64 z) z) y) y)
211.0ms	(*.f64 (-.f64 (log.f64 z) z) y)
95.0ms	(fma.f64 x 1/2 (+.f64 (*.f64 (-.f64 (log.f64 z) z) y) y))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
6×	`pow1_binary64`
5×	`add-cube-cbrt_binary64`

Counts

3 → 51

Calls

3 calls:

5.0ms	(+.f64 (*.f64 (-.f64 (log.f64 z) z) y) y)
5.0ms	(*.f64 (-.f64 (log.f64 z) z) y)
0.0ms	(fma.f64 x 1/2 (+.f64 (*.f64 (-.f64 (log.f64 z) z) y) y))

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

603×	`fma-neg_binary64`
402×	`distribute-rgt-in_binary64`
380×	`fma-def_binary64`
374×	`distribute-lft-in_binary64`
326×	`associate-l_binary64`

Counts

135 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1920
1	309	1585
2	877	1575
3	3035	1575
4	4611	1575
5	4987	1575

prune147.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	148	7	155

Error

Counts

155 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (+.f64 (*.f64 (-.f64 (log.f64 z) z) y) y))
	0.1b	(fma.f64 x 1/2 (+.f64 (.f64 y (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))) y))
	0.4b	(fma.f64 x 1/2 (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (log.f64 z)) (cbrt.f64 (log.f64 z))) (cbrt.f64 (log.f64 z)) (neg.f64 z)) y) y))
	0.2b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (fma.f64 1 (log.f64 (cbrt.f64 z)) (neg.f64 (.f64 (sqrt.f64 z) (sqrt.f64 z))))) (fma.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sqrt.f64 z)))) y))
	0.1b	(fma.f64 x 1/2 (+.f64 (fma.f64 (log.f64 (.f64 (pow.f64 z 2/3) (pow.f64 (cbrt.f64 -1) 2))) y y) (.f64 y (-.f64 (log.f64 (*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))) z))))
	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y))
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (log.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))))) (-.f64 (log.f64 (cbrt.f64 (cbrt.f64 z))) z)) y))

Compiler

Compiled 2793 to 1008 computations (63.9% saved)

regimes1.6s (19.1%)

Accuracy

Total 0.1b remaining (84.6%)

Threshold costs 0.1b (84.6%)

Counts

165 → 1

Compiler

Compiled 24529 to 14407 computations (41.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`cancel-sign-sub-inv_binary64`
5×	`sub-neg_binary64`
4×	`+-commutative_binary64`
4×	`distribute-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	15	16
2	23	16
3	35	14
4	47	14
5	50	14
6	46	14

end140.0ms (1.6%)

Compiler: Compiled 211 to 123 computations (41.7% saved)

Details

analyze257.0ms (3%)

sample1.4s (16.4%)

simplify287.0ms (3.4%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series321.0ms (3.8%)

rewrite8.0ms (0.1%)

simplify134.0ms (1.6%)

prune80.0ms (0.9%)

localize13.0ms (0.2%)

series2.0s (23.2%)

rewrite27.0ms (0.3%)

simplify95.0ms (1.1%)

prune275.0ms (3.2%)

localize20.0ms (0.2%)

series604.0ms (7.1%)

rewrite4.0ms (0.1%)

simplify106.0ms (1.2%)

prune346.0ms (4.1%)

localize8.0ms (0.1%)

series518.0ms (6.1%)

rewrite13.0ms (0.2%)

simplify99.0ms (1.2%)

prune147.0ms (1.7%)

regimes1.6s (19.1%)

simplify3.0ms (0%)

end140.0ms (1.6%)

Profiling