Details

analyze251.0ms (3.6%)

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 (19.1%)

Results

1.0s	8256×	body	128	valid
47.0ms	376×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify284.0ms (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 2 expressions with local error:

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

series213.0ms (3%)

Counts

2 → 33

Calls

2 calls:

208.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
5.0ms	(-.f64 (log.f64 z) z)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
12×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`

Counts

2 → 48

Calls

2 calls:

4.0ms	(-.f64 (log.f64 z) z)
0.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)

simplify125.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-neg_binary64`
428×	`fma-def_binary64`
345×	`exp-prod_binary64`
341×	`associate-l_binary64`
295×	`exp-sum_binary64`

Counts

81 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	924
1	223	740
2	668	702
3	2728	702
4	4092	702
5	4913	702
6	4964	702
7	4983	702
8	4872	702

prune99.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	6	67

Error

0.0b

Counts

67 → 6

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))
	15.9b	(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))
	15.9b	(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))
	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))))
	25.2b	(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))))
▶	0.1b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z))))

Compiler

Compiled 1428 to 546 computations (61.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 1 z))
✓	0.0b	(+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z))
✓	0.2b	(-.f64 y (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z)))
✓	0.3b	(*.f64 (log.f64 (/.f64 1 z)) y)

series833.0ms (11.9%)

Counts

4 → 58

Calls

4 calls:

285.0ms	(-.f64 y (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z)))
267.0ms	(+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z))
260.0ms	(*.f64 (log.f64 (/.f64 1 z)) y)
20.0ms	(log.f64 (/.f64 1 z))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
13×	`log-prod_binary64`
11×	`add-log-exp_binary64`

Counts

4 → 101

Calls

4 calls:

5.0ms	(-.f64 y (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z)))
4.0ms	(+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z))
3.0ms	(*.f64 (log.f64 (/.f64 1 z)) y)
2.0ms	(log.f64 (/.f64 1 z))

simplify96.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

740×	`unsub-neg_binary64`
301×	`*-commutative_binary64`
295×	`distribute-rgt-in_binary64`
262×	`cancel-sign-sub-inv_binary64`
255×	`distribute-lft-in_binary64`

Counts

159 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	2406
1	369	1963
2	1328	1765
3	3875	1758
4	5046	1758

prune255.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	163	7	170

Error

0.0b

Counts

170 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z))))
	29.0b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (exp.f64 (log.f64 (neg.f64 (log.f64 z)))) y) (.f64 y z))))
	15.9b	(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))
	17.4b	(fma.f64 x 1/2 (-.f64 y (+.f64 (cbrt.f64 (pow.f64 (neg.f64 (.f64 (log.f64 z) y)) 3)) (.f64 y z))))
	15.9b	(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))
	0.4b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (.f64 (neg.f64 (log.f64 z)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 y z))))
▶	0.3b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (.f64 (.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z)))) (cbrt.f64 (neg.f64 (log.f64 z)))) y) (.f64 y z))))

Compiler

Compiled 4139 to 2198 computations (46.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (*.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z)))) (cbrt.f64 (neg.f64 (log.f64 z)))) y)
✓	0.4b	(.f64 (.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z)))) (cbrt.f64 (neg.f64 (log.f64 z))))
✓	0.5b	(*.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z))))
✓	0.5b	(cbrt.f64 (neg.f64 (log.f64 z)))

series1.2s (16.7%)

Counts

4 → 60

Calls

4 calls:

426.0ms	(*.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z))))
386.0ms	(cbrt.f64 (neg.f64 (log.f64 z)))
300.0ms	(.f64 (.f64 (*.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z)))) (cbrt.f64 (neg.f64 (log.f64 z)))) y)
62.0ms	(.f64 (.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z)))) (cbrt.f64 (neg.f64 (log.f64 z))))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`cbrt-prod_binary64`
57×	`pow1_binary64`
38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
33×	`associate-r_binary64`

Counts

4 → 169

Calls

4 calls:

12.0ms	(.f64 (.f64 (*.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z)))) (cbrt.f64 (neg.f64 (log.f64 z)))) y)
11.0ms	(*.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z))))
10.0ms	(.f64 (.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z)))) (cbrt.f64 (neg.f64 (log.f64 z))))
1.0ms	(cbrt.f64 (neg.f64 (log.f64 z)))

simplify155.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-def_binary64`
379×	`*-commutative_binary64`
354×	`distribute-rgt-neg-in_binary64`
320×	`log-prod_binary64`
307×	`distribute-lft-neg-out_binary64`

Counts

229 → 205

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	165	3082
1	301	2922
2	1060	2537
3	2087	2487
4	3734	2263
5	4790	2263
6	4840	2263

prune315.0ms (4.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	258	8	266

Error

Counts

266 → 8

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (.f64 (pow.f64 (pow.f64 (log.f64 z) 2) 1/3) (cbrt.f64 (neg.f64 (log.f64 z)))) y) (*.f64 y z))))
✓	0.3b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (.f64 (.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z)))) (cbrt.f64 (neg.f64 (log.f64 z)))) y) (.f64 y z))))
✓	0.1b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z))))
	29.0b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (exp.f64 (log.f64 (neg.f64 (log.f64 z)))) y) (.f64 y z))))
	15.9b	(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))
	17.4b	(fma.f64 x 1/2 (-.f64 y (+.f64 (cbrt.f64 (pow.f64 (neg.f64 (.f64 (log.f64 z) y)) 3)) (.f64 y z))))
	15.9b	(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))
	0.4b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (.f64 (neg.f64 (log.f64 z)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 y z))))

Compiler

Compiled 7921 to 2444 computations (69.1% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 (pow.f64 (log.f64 z) 2) 1/3) (cbrt.f64 (neg.f64 (log.f64 z))))
✓	0.5b	(pow.f64 (log.f64 z) 2)
	0.5b	(cbrt.f64 (neg.f64 (log.f64 z)))
✓	1.1b	(pow.f64 (pow.f64 (log.f64 z) 2) 1/3)

series421.0ms (6%)

Counts

3 → 28

Calls

3 calls:

356.0ms	(pow.f64 (pow.f64 (log.f64 z) 2) 1/3)
39.0ms	(*.f64 (pow.f64 (pow.f64 (log.f64 z) 2) 1/3) (cbrt.f64 (neg.f64 (log.f64 z))))
25.0ms	(pow.f64 (log.f64 z) 2)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`unpow-prod-down_binary64`
33×	`add-sqr-sqrt_binary64`
18×	`cbrt-prod_binary64`
15×	`associate-r_binary64`
15×	`*-un-lft-identity_binary64`

Counts

3 → 107

Calls

3 calls:

11.0ms	(*.f64 (pow.f64 (pow.f64 (log.f64 z) 2) 1/3) (cbrt.f64 (neg.f64 (log.f64 z))))
3.0ms	(pow.f64 (pow.f64 (log.f64 z) 2) 1/3)
2.0ms	(pow.f64 (log.f64 z) 2)

simplify148.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

768×	`log-prod_binary64`
765×	`fma-neg_binary64`
572×	`exp-prod_binary64`
425×	`cube-prod_binary64`
359×	`*-commutative_binary64`

Counts

135 → 148

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	145	1940
1	280	1674
2	729	1663
3	1341	1537
4	2505	1047
5	3205	998
6	3470	998
7	4385	998
8	4944	998

prune213.0ms (3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	175	8	183

Error

Counts

183 → 8

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (.f64 (pow.f64 (pow.f64 (log.f64 z) 2) 1/3) (cbrt.f64 (neg.f64 (log.f64 z)))) y) (*.f64 y z))))
✓	0.3b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (.f64 (.f64 (cbrt.f64 (neg.f64 (log.f64 z))) (cbrt.f64 (neg.f64 (log.f64 z)))) (cbrt.f64 (neg.f64 (log.f64 z)))) y) (.f64 y z))))
✓	0.1b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z))))
	29.0b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (exp.f64 (log.f64 (neg.f64 (log.f64 z)))) y) (.f64 y z))))
	15.9b	(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))
	17.4b	(fma.f64 x 1/2 (-.f64 y (+.f64 (cbrt.f64 (pow.f64 (neg.f64 (.f64 (log.f64 z) y)) 3)) (.f64 y z))))
	15.9b	(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))
	0.4b	(fma.f64 x 1/2 (-.f64 y (+.f64 (.f64 (.f64 (neg.f64 (log.f64 z)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 y z))))

Compiler

Compiled 4913 to 2427 computations (50.6% saved)

regimes819.0ms (11.7%)

Accuracy

Total 0.1b remaining (62.7%)

Threshold costs 0.1b (62.7%)

Counts

110 → 1

Compiler

Compiled 15912 to 10188 computations (36% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-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	11	16
1	17	16
2	21	16
3	23	16
4	24	16
5	23	16

end132.0ms (1.9%)

Compiler: Compiled 214 to 131 computations (38.8% saved)

Details

analyze251.0ms (3.6%)

sample1.3s (19.1%)

simplify284.0ms (4%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series213.0ms (3%)

rewrite7.0ms (0.1%)

simplify125.0ms (1.8%)

prune99.0ms (1.4%)

localize11.0ms (0.2%)

series833.0ms (11.9%)

rewrite20.0ms (0.3%)

simplify96.0ms (1.4%)

prune255.0ms (3.6%)

localize15.0ms (0.2%)

series1.2s (16.7%)

rewrite47.0ms (0.7%)

simplify155.0ms (2.2%)

prune315.0ms (4.5%)

localize20.0ms (0.3%)

series421.0ms (6%)

rewrite21.0ms (0.3%)

simplify148.0ms (2.1%)

prune213.0ms (3%)

regimes819.0ms (11.7%)

simplify2.0ms (0%)

end132.0ms (1.9%)

Profiling