Details

analyze242.0ms (4%)

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 (21.2%)

Results

995.0ms	8256×	body	128	valid
43.0ms	388×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify285.0ms (4.7%)

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)

localize7.0ms (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)

series266.0ms (4.4%)

Counts

3 → 69

Calls

3 calls:

184.0ms	(fma.f64 y (-.f64 (log.f64 z) z) y)
78.0ms	(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))

simplify123.0ms (2%)

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

prune73.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	0	0
Picked	1	0	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 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z)) y))
	32.1b	(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))))
	0.1b	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
▶	0.1b	(+.f64 (*.f64 x 1/2) (fma.f64 y (-.f64 (log.f64 z) z) y))

Compiler

Compiled 1740 to 650 computations (62.6% 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	(+.f64 (*.f64 x 1/2) (fma.f64 y (-.f64 (log.f64 z) z) y))
	0.2b	(fma.f64 y (-.f64 (log.f64 z) z) y)

series79.0ms (1.3%)

Counts

1 → 36

Calls

1 calls:

79.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`+-commutative_binary64`
1×	`associate-+r+_binary64`
1×	`fma-udef_binary64`
1×	`flip-+_binary64`

Counts

1 → 15

Calls

1 calls:

3.0ms

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

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

364×	`neg-mul-1_binary64`
336×	`cancel-sign-sub-inv_binary64`
309×	`associate--r+_binary64`
265×	`distribute-rgt-in_binary64`
254×	`fma-def_binary64`

Counts

51 → 39

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	940
1	207	824
2	585	767
3	2166	767
4	4468	767
5	5137	767

prune79.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	105	5	110

Error

0.0b

Counts

110 → 5

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))
	32.1b	(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))))
	0.1b	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
✓	0.1b	(+.f64 (*.f64 x 1/2) (fma.f64 y (-.f64 (log.f64 z) z) y))

Compiler

Compiled 2042 to 812 computations (60.2% saved)

localize13.0ms (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))
✓	0.5b	(cbrt.f64 z)

series1.9s (31.2%)

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)
237.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (-.f64 (log.f64 (cbrt.f64 z)) z))
34.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
28.0ms	(cbrt.f64 z)

rewrite27.0ms (0.4%)

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:

14.0ms	(+.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)

simplify88.0ms (1.5%)

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

prune191.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	221	3	224
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	224	5	229

Error

Counts

229 → 5

Alt Table

Status	Error	Program
	16.1b	(fma.f64 x 1/2 (+.f64 y (+.f64 (.f64 y (log.f64 (pow.f64 z 2/3))) (.f64 y (log.f64 (pow.f64 z 1/3))))))
✓	0.1b	(+.f64 (*.f64 x 1/2) (fma.f64 y (-.f64 (log.f64 z) z) 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))
▶	0.1b	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
	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))

Compiler

Compiled 5278 to 1819 computations (65.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
✓	0.1b	(+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x)))
✓	0.3b	(*.f64 (log.f64 z) y)

series371.0ms (6.1%)

Counts

3 → 37

Calls

3 calls:

191.0ms	(*.f64 (log.f64 z) y)
98.0ms	(+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x)))
81.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-log-exp_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
6×	`sum-log_binary64`

Counts

3 → 60

Calls

3 calls:

6.0ms	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))
4.0ms	(+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x)))
3.0ms	(*.f64 (log.f64 z) y)

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-neg_binary64`
659×	`fma-def_binary64`
513×	`distribute-rgt-in_binary64`
479×	`distribute-lft-in_binary64`
248×	`associate-+l+_binary64`

Counts

97 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1520
1	358	1254
2	1133	1205
3	4590	1205
4	5115	1205

prune87.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	113	5	118

Error

Counts

118 → 5

Alt Table

Status	Error	Program
	16.1b	(fma.f64 x 1/2 (+.f64 y (+.f64 (.f64 y (log.f64 (pow.f64 z 2/3))) (.f64 y (log.f64 (pow.f64 z 1/3))))))
✓	0.1b	(+.f64 (*.f64 x 1/2) (fma.f64 y (-.f64 (log.f64 z) z) 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))
	0.3b	(-.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))
✓	0.1b	(-.f64 (+.f64 (.f64 (log.f64 z) y) (+.f64 y (.f64 1/2 x))) (*.f64 y z))

Compiler

Compiled 2404 to 1023 computations (57.4% saved)

regimes699.0ms (11.5%)

Accuracy

Total 0.1b remaining (69.4%)

Threshold costs 0.1b (69.4%)

Counts

92 → 1

Compiler

Compiled 11137 to 6968 computations (37.4% saved)

simplify5.0ms (0.1%)

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

end81.0ms (1.3%)

Compiler: Compiled 128 to 80 computations (37.5% saved)

Details

analyze242.0ms (4%)

sample1.3s (21.2%)

simplify285.0ms (4.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series266.0ms (4.4%)

rewrite6.0ms (0.1%)

simplify123.0ms (2%)

prune73.0ms (1.2%)

localize8.0ms (0.1%)

series79.0ms (1.3%)

rewrite3.0ms (0.1%)

simplify65.0ms (1.1%)

prune79.0ms (1.3%)

localize13.0ms (0.2%)

series1.9s (31.2%)

rewrite27.0ms (0.4%)

simplify88.0ms (1.5%)

prune191.0ms (3.1%)

localize9.0ms (0.2%)

series371.0ms (6.1%)

rewrite15.0ms (0.3%)

simplify71.0ms (1.2%)

prune87.0ms (1.4%)

regimes699.0ms (11.5%)

simplify5.0ms (0.1%)

end81.0ms (1.3%)

Profiling