Details

analyze260.0ms (3.2%)

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 (17.1%)

Results

1.1s	8256×	body	128	valid
46.0ms	370×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify292.0ms (3.6%)

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)

localize9.0ms (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)
✓	0.2b	(fma.f64 y (-.f64 (log.f64 z) z) y)

series302.0ms (3.7%)

Counts

3 → 69

Calls

3 calls:

206.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
89.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
5.0ms	(-.f64 (log.f64 z) z)

rewrite9.0ms (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:

6.0ms	(-.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))

simplify133.0ms (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 (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Error

0.0b

Counts

94 → 4

Alt Table

Status	Error	Program
	14.7b	(fma.f64 x 1/2 (fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (log.f64 z) z) 3)) y))
	21.1b	(fma.f64 x 1/2 (+.f64 (*.f64 (log.f64 z) y) y))
	33.4b	(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))))
▶	0.1b	(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))

Compiler

Compiled 1670 to 626 computations (62.5% saved)

localize14.0ms (0.2%)

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	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series1.8s (22%)

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)
242.0ms	(+.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:

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)

simplify92.0ms (1.1%)

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

prune226.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	220	4	224
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	224	4	228

Error

0.0b

Counts

228 → 4

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 z) (neg.f64 z)) y))
	0.9b	(fma.f64 x 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)) (cbrt.f64 (fma.f64 y (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))) (cbrt.f64 (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 (*.f64 y (-.f64 (log.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 (neg.f64 z)) (cbrt.f64 -1))) z))))

Compiler

Compiled 5298 to 1816 computations (65.7% saved)

localize9.0ms (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) (neg.f64 z)) y))
✓	0.0b	(+.f64 (log.f64 z) (neg.f64 z))
✓	0.2b	(fma.f64 y (+.f64 (log.f64 z) (neg.f64 z)) y)

series283.0ms (3.5%)

Counts

3 → 72

Calls

3 calls:

192.0ms	(fma.f64 y (+.f64 (log.f64 z) (neg.f64 z)) y)
86.0ms	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 z) (neg.f64 z)) y))
5.0ms	(+.f64 (log.f64 z) (neg.f64 z))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
6×	`pow1_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms	(+.f64 (log.f64 z) (neg.f64 z))
0.0ms	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 z) (neg.f64 z)) y))
0.0ms	(fma.f64 y (+.f64 (log.f64 z) (neg.f64 z)) y)

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

446×	`fma-neg_binary64`
413×	`exp-sum_binary64`
345×	`fma-def_binary64`
308×	`times-frac_binary64`
288×	`distribute-rgt-in_binary64`

Counts

119 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1487
1	268	1226
2	715	1223
3	2268	1223
4	4041	1223
5	4944	1223

prune63.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	95	4	99

Error

0.0b

Counts

99 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (log.f64 z) (neg.f64 z)) y))
	0.9b	(fma.f64 x 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)) (cbrt.f64 (fma.f64 y (+.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))) (cbrt.f64 (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 (*.f64 y (-.f64 (log.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 (neg.f64 z)) (cbrt.f64 -1))) z))))

Compiler

Compiled 1658 to 621 computations (62.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 1/2 (+.f64 (*.f64 y (-.f64 (log.f64 z) z)) y))
	0.0b	(-.f64 (log.f64 z) z)
✓	0.1b	(+.f64 (*.f64 y (-.f64 (log.f64 z) z)) y)
✓	0.2b	(*.f64 y (-.f64 (log.f64 z) z))

series475.0ms (5.9%)

Counts

3 → 72

Calls

3 calls:

195.0ms	(+.f64 (*.f64 y (-.f64 (log.f64 z) z)) y)
193.0ms	(*.f64 y (-.f64 (log.f64 z) z))
87.0ms	(fma.f64 x 1/2 (+.f64 (*.f64 y (-.f64 (log.f64 z) z)) y))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`prod-diff_binary64`
45×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
38×	`associate-+l+_binary64`

Counts

3 → 125

Calls

3 calls:

8.0ms	(+.f64 (*.f64 y (-.f64 (log.f64 z) z)) y)
7.0ms	(*.f64 y (-.f64 (log.f64 z) z))
0.0ms	(fma.f64 x 1/2 (+.f64 (*.f64 y (-.f64 (log.f64 z) z)) y))

simplify146.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1000×	`fma-neg_binary64`
442×	`distribute-rgt-in_binary64`
404×	`distribute-lft-in_binary64`
242×	`*-commutative_binary64`
179×	`cancel-sign-sub-inv_binary64`

Counts

197 → 190

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	223	2673
1	419	2274
2	1319	2107
3	3616	2101
4	4865	2101
5	4938	2101
6	4895	2101

prune185.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	234	1	235
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	235	4	239

Error

0.0b

Counts

239 → 4

Alt Table

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

Compiler

Compiled 4886 to 1531 computations (68.7% saved)

regimes2.1s (26%)

Accuracy

Total 0.1b remaining (80.5%)

Threshold costs 0.1b (80.5%)

Counts

200 → 1

Compiler

Compiled 30808 to 18329 computations (40.5% 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	12	18
1	20	18
2	24	18
3	26	18
4	27	18
5	26	18

end77.0ms (1%)

Compiler: Compiled 111 to 76 computations (31.5% saved)

Details

analyze260.0ms (3.2%)

sample1.4s (17.1%)

simplify292.0ms (3.6%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series302.0ms (3.7%)

rewrite9.0ms (0.1%)

simplify133.0ms (1.6%)

prune67.0ms (0.8%)

localize14.0ms (0.2%)

series1.8s (22%)

rewrite27.0ms (0.3%)

simplify92.0ms (1.1%)

prune226.0ms (2.8%)

localize9.0ms (0.1%)

series283.0ms (3.5%)

rewrite7.0ms (0.1%)

simplify85.0ms (1.1%)

prune63.0ms (0.8%)

localize10.0ms (0.1%)

series475.0ms (5.9%)

rewrite28.0ms (0.3%)

simplify146.0ms (1.8%)

prune185.0ms (2.3%)

regimes2.1s (26%)

simplify3.0ms (0%)

end77.0ms (1%)

Profiling