Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	50%	25%	3
37.5%	25%	37.5%	4
43.7%	12.5%	43.8%	5
46.9%	6.2%	46.9%	6
48.4%	3.1%	48.5%	7
49.2%	1.6%	49.2%	8
49.6%	0.8%	49.6%	9
49.6%	0.4%	50%	10
49.7%	0.2%	50.1%	11
49.7%	0.1%	50.2%	12
49.7%	0%	50.2%	13
49.7%	0%	50.2%	14

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample750.0ms (14.2%)

Results

720.0ms	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6
2	5	6

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 x (log.f64 x))

Compiler

Compiled 15 to 9 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (log.f64 x))

series29.0ms (0.6%)

Counts

1 → 12

Calls

1 calls:

29.0ms

(*.f64 x (log.f64 x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
4×	`associate-r_binary64`

Counts

1 → 27

Calls

1 calls:

3.0ms

(*.f64 x (log.f64 x))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1025×	`fma-def_binary64`
501×	`sub-neg_binary64`
395×	`div-sub_binary64`
347×	`fma-neg_binary64`
343×	`distribute-rgt-neg-out_binary64`

Counts

39 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	359
1	96	325
2	258	325
3	452	325
4	1256	325
5	2761	325
6	4564	325
7	5019	325

prune21.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	28	5	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	6	34

Error

0.0b

Counts

34 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (log.f64 x)))
▶	0.4b	(+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x) (*.f64 (log.f64 (cbrt.f64 x)) x))
	36.2b	(.f64 (sqrt.f64 (.f64 x (log.f64 x))) (sqrt.f64 (*.f64 x (log.f64 x))))
	40.1b	(cbrt.f64 (.f64 (.f64 (.f64 x (log.f64 x)) (.f64 x (log.f64 x))) (*.f64 x (log.f64 x))))
✓	0.2b	(*.f64 x (log.f64 x))

Compiler

Compiled 437 to 164 computations (62.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (log.f64 (cbrt.f64 x)) x)
✓	0.3b	(+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x) (*.f64 (log.f64 (cbrt.f64 x)) x))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(cbrt.f64 x)

series2.0s (37.7%)

Counts

4 → 48

Calls

4 calls:

1.3s	(+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x) (*.f64 (log.f64 (cbrt.f64 x)) x))
584.0ms	(*.f64 (log.f64 (cbrt.f64 x)) x)
40.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
31.0ms	(cbrt.f64 x)

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
14×	`pow1_binary64`

Counts

4 → 92

Calls

4 calls:

6.0ms	(+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x) (*.f64 (log.f64 (cbrt.f64 x)) x))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
3.0ms	(*.f64 (log.f64 (cbrt.f64 x)) x)
1.0ms	(cbrt.f64 x)

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
421×	`fma-def_binary64`
397×	`distribute-rgt-in_binary64`
345×	`distribute-lft-in_binary64`
266×	`log-prod_binary64`

Counts

140 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1674
1	294	1361
2	1135	1227
3	4063	1227
4	4904	1227

prune99.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	180	8	188

Error

0.0b

Counts

188 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	0.8b	(+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x) (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 (cbrt.f64 x)) x)) (cbrt.f64 (.f64 (log.f64 (cbrt.f64 x)) x))) (cbrt.f64 (*.f64 (log.f64 (cbrt.f64 x)) x))))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (log.f64 x)))
	0.3b	(+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x) (*.f64 (log.f64 (pow.f64 x 1/3)) x))
▶	0.2b	(fma.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x (.f64 (log.f64 (cbrt.f64 x)) x))
	36.2b	(.f64 (sqrt.f64 (.f64 x (log.f64 x))) (sqrt.f64 (*.f64 x (log.f64 x))))
	40.1b	(cbrt.f64 (.f64 (.f64 (.f64 x (log.f64 x)) (.f64 x (log.f64 x))) (*.f64 x (log.f64 x))))
✓	0.2b	(*.f64 x (log.f64 x))

Compiler

Compiled 3594 to 1038 computations (71.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x (.f64 (log.f64 (cbrt.f64 x)) x))
	0.2b	(*.f64 (log.f64 (cbrt.f64 x)) x)
	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
	0.5b	(cbrt.f64 x)

series1.5s (28.6%)

Counts

1 → 12

Calls

1 calls:

1.5s	(fma.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x (.f64 (log.f64 (cbrt.f64 x)) x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (log.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) x (*.f64 (log.f64 (cbrt.f64 x)) x))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

455×	`fma-neg_binary64`
383×	`fma-def_binary64`
367×	`distribute-rgt-in_binary64`
358×	`unswap-sqr_binary64`
348×	`distribute-lft-in_binary64`

Counts

22 → 23

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	497
1	101	326
2	237	264
3	799	236
4	3098	236
5	4799	236
6	5101	236

prune125.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	172	3	175
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	176	7	183

Error

0.0b

Counts

183 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	0.4b	(+.f64 (.f64 x (log.f64 (pow.f64 x 2/3))) (.f64 (log.f64 (cbrt.f64 x)) x))
▶	0.2b	(fma.f64 (log.f64 (.f64 (cbrt.f64 x) (pow.f64 x 1/3))) x (.f64 (log.f64 (cbrt.f64 x)) x))
	0.7b	(fma.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x (.f64 (.f64 (cbrt.f64 (.f64 x (log.f64 (cbrt.f64 x)))) (cbrt.f64 (.f64 x (log.f64 (cbrt.f64 x))))) (cbrt.f64 (.f64 x (log.f64 (cbrt.f64 x))))))
✓	0.2b	(fma.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x (.f64 (log.f64 (cbrt.f64 x)) x))
	36.2b	(.f64 (sqrt.f64 (.f64 x (log.f64 x))) (sqrt.f64 (*.f64 x (log.f64 x))))
✓	0.2b	(*.f64 x (log.f64 x))

Compiler

Compiled 3197 to 901 computations (71.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (log.f64 (cbrt.f64 x)) x)
✓	0.5b	(*.f64 (cbrt.f64 x) (pow.f64 x 1/3))
	0.5b	(cbrt.f64 x)
✓	5.1b	(pow.f64 x 1/3)

series63.0ms (1.2%)

Counts

2 → 16

Calls

2 calls:

31.0ms	(*.f64 (cbrt.f64 x) (pow.f64 x 1/3))
23.0ms	(pow.f64 x 1/3)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`unpow-prod-down_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 57

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 x) (pow.f64 x 1/3))
1.0ms	(pow.f64 x 1/3)

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

827×	`log-prod_binary64`
716×	`unswap-sqr_binary64`
412×	`*-commutative_binary64`
339×	`associate-l_binary64`
311×	`exp-sum_binary64`

Counts

73 → 86

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	86	779
1	145	752
2	408	526
3	1318	426
4	3243	385
5	4556	373
6	5367	373

prune126.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	162	6	168

Error

0.0b

Counts

168 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	0.4b	(+.f64 (.f64 x (log.f64 (pow.f64 x 2/3))) (.f64 (log.f64 (cbrt.f64 x)) x))
✓	0.2b	(fma.f64 (log.f64 (.f64 (cbrt.f64 x) (pow.f64 x 1/3))) x (.f64 (log.f64 (cbrt.f64 x)) x))
	0.7b	(fma.f64 (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) x (.f64 (.f64 (cbrt.f64 (.f64 x (log.f64 (cbrt.f64 x)))) (cbrt.f64 (.f64 x (log.f64 (cbrt.f64 x))))) (cbrt.f64 (.f64 x (log.f64 (cbrt.f64 x))))))
	0.2b	(fma.f64 (log.f64 (.f64 (pow.f64 (cbrt.f64 x) 5/3) (cbrt.f64 (pow.f64 x 1/3)))) x (.f64 (log.f64 (cbrt.f64 x)) x))
✓	0.2b	(*.f64 x (log.f64 x))

Compiler

Compiled 3021 to 1299 computations (57% saved)

regimes119.0ms (2.3%)

Accuracy

Total 0.3b remaining (94.9%)

Threshold costs 0.3b (94.9%)

Counts

58 → 1

Compiler

Compiled 1917 to 1108 computations (42.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	27
1	15	27
2	15	27

end93.0ms (1.8%)

Compiler: Compiled 125 to 72 computations (42.4% saved)

Details

analyze4.0ms (0.1%)

sample750.0ms (14.2%)

simplify5.0ms (0.1%)

prune3.0ms (0%)

localize3.0ms (0.1%)

series29.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify66.0ms (1.3%)

prune21.0ms (0.4%)

localize9.0ms (0.2%)

series2.0s (37.7%)

rewrite17.0ms (0.3%)

simplify77.0ms (1.5%)

prune99.0ms (1.9%)

localize9.0ms (0.2%)

series1.5s (28.6%)

rewrite1.0ms (0%)

simplify61.0ms (1.1%)

prune125.0ms (2.4%)

localize12.0ms (0.2%)

series63.0ms (1.2%)

rewrite9.0ms (0.2%)

simplify76.0ms (1.4%)

prune126.0ms (2.4%)

regimes119.0ms (2.3%)

simplify2.0ms (0%)

end93.0ms (1.8%)

Profiling