Details

analyze112.0ms (0.9%)

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
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
49.9%	25%	25.1%	7
49.9%	25%	25.1%	8
49.9%	25%	25.1%	9
49.9%	12.5%	37.6%	10
49.9%	12.5%	37.6%	11
49.9%	12.5%	37.6%	12
49.9%	6.2%	43.8%	13
49.9%	6.2%	43.8%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample1.2s (9.6%)

Infinites

12.8% of outputs are infinite.

Results

802.0ms	8256×	body	128	valid
102.0ms	1115×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify293.0ms (2.4%)

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

series279.0ms (2.3%)

Counts

3 → 69

Calls

3 calls:

197.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
77.0ms	(fma.f64 x 1/2 (fma.f64 y (-.f64 (log.f64 z) z) y))
4.0ms	(-.f64 (log.f64 z) z)

rewrite6.0ms (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:

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))

simplify127.0ms (1%)

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

prune71.0ms (0.6%)

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 (fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	0.3b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	34.3b	(cbrt.f64 (pow.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	33.6b	(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))))
	0.6b	(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))))
	25.0b	(fma.f64 y (log.f64 z) (fma.f64 1/2 x y))

Compiler

Compiled 1764 to 666 computations (62.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series1.9s (15.7%)

Counts

4 → 60

Calls

4 calls:

1.6s	(fma.f64 y (+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y)
276.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
35.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
30.0ms	(cbrt.f64 z)

rewrite25.0ms (0.2%)

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)

simplify93.0ms (0.8%)

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

prune288.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	220	4	224
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	224	6	230

Error

0.0b

Counts

230 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (.f64 (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))))) (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	0.3b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	34.3b	(cbrt.f64 (pow.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	0.3b	(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))))
▶	0.1b	(fma.f64 x 1/2 (fma.f64 y (+.f64 (fma.f64 2/3 (log.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 5376 to 1880 computations (65% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y)
✓	0.1b	(+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z))
✓	0.3b	(fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z))))
✓	0.6b	(cbrt.f64 (sqrt.f64 z))

series1.5s (12.4%)

Counts

4 → 46

Calls

4 calls:

1.2s	(fma.f64 y (+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y)
207.0ms	(fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z))))
90.0ms	(+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z))
21.0ms	(cbrt.f64 (sqrt.f64 z))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`associate-+r+_binary64`
26×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
15×	`prod-diff_binary64`

Counts

4 → 86

Calls

4 calls:

7.0ms	(+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z))
1.0ms	(cbrt.f64 (sqrt.f64 z))
0.0ms	(fma.f64 y (+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y)
0.0ms	(fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z))))

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-neg_binary64`
681×	`fma-def_binary64`
449×	`distribute-rgt-in_binary64`
404×	`associate-l_binary64`
399×	`distribute-lft-in_binary64`

Counts

132 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	168	2767
1	344	2343
2	1072	2036
3	4389	2030
4	4965	2030

prune219.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	154	6	160

Error

Counts

160 → 6

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (.f64 (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))))) (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	0.3b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	34.3b	(cbrt.f64 (pow.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	0.3b	(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))))
	0.6b	(fma.f64 x 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y)) (cbrt.f64 (fma.f64 y (+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y))) (cbrt.f64 (fma.f64 y (+.f64 (fma.f64 2/3 (log.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 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y))

Compiler

Compiled 4602 to 1716 computations (62.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))))
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.5b	(cbrt.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
	0.6b	(cbrt.f64 z)

series3.1s (25.1%)

Counts

2 → 24

Calls

2 calls:

1.6s	(cbrt.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
1.4s	(.f64 (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-prod_binary64`
67×	`pow1_binary64`
57×	`log-pow_binary64`
37×	`pow1/3_binary64`
23×	`swap-sqr_binary64`

Counts

2 → 99

Calls

2 calls:

11.0ms	(.f64 (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))))
5.0ms	(cbrt.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

simplify133.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

410×	`*-commutative_binary64`
402×	`log-prod_binary64`
385×	`unswap-sqr_binary64`
312×	`fma-def_binary64`
307×	`distribute-rgt-out_binary64`

Counts

123 → 121

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	2173
1	175	1826
2	416	1629
3	1187	1605
4	2637	1443
5	4165	1443
6	4645	1443
7	4844	1443

prune739.0ms (6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	488	0	488
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	488	6	494

Error

Counts

494 → 6

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 x 1/2 (fma.f64 y (fma.f64 (.f64 (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))))) (cbrt.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	0.3b	(fma.f64 x 1/2 (-.f64 (+.f64 (.f64 (log.f64 z) y) y) (.f64 y z)))
	34.3b	(cbrt.f64 (pow.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	0.3b	(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))))
	0.6b	(fma.f64 x 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y)) (cbrt.f64 (fma.f64 y (+.f64 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y))) (cbrt.f64 (fma.f64 y (+.f64 (fma.f64 2/3 (log.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 (fma.f64 2/3 (log.f64 z) (log.f64 (cbrt.f64 (sqrt.f64 z)))) (-.f64 (log.f64 (cbrt.f64 (sqrt.f64 z))) z)) y))

Compiler

Compiled 18775 to 4344 computations (76.9% saved)

regimes1.9s (15.3%)

Accuracy

Total 0.1b remaining (78.5%)

Threshold costs 0.1b (78.5%)

Counts

221 → 1

Compiler

Compiled 37459 to 22935 computations (38.8% 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

end117.0ms (1%)

Compiler: Compiled 214 to 115 computations (46.3% saved)

Details

analyze112.0ms (0.9%)

sample1.2s (9.6%)

simplify293.0ms (2.4%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series279.0ms (2.3%)

rewrite6.0ms (0.1%)

simplify127.0ms (1%)

prune71.0ms (0.6%)

localize14.0ms (0.1%)

series1.9s (15.7%)

rewrite25.0ms (0.2%)

simplify93.0ms (0.8%)

prune288.0ms (2.3%)

localize17.0ms (0.1%)

series1.5s (12.4%)

rewrite14.0ms (0.1%)

simplify92.0ms (0.7%)

prune219.0ms (1.8%)

localize16.0ms (0.1%)

series3.1s (25.1%)

rewrite26.0ms (0.2%)

simplify133.0ms (1.1%)

prune739.0ms (6%)

regimes1.9s (15.3%)

simplify3.0ms (0%)

end117.0ms (1%)

Profiling