Details

analyze21.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample18.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.9b	(/.f64 (atan2.f64 im re) (log.f64 10))

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.9b	(/.f64 (atan2.f64 im re) (log.f64 10))

rewrite34.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

12×	`times-frac_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
5×	`pow1_binary64`
4×	`log-pow_binary64` `associate-/r*_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`

Counts

1 → 31

Calls

1 calls:

3.0ms

(/.f64 (atan2.f64 im re) (log.f64 10))

Compiler

Compiled 369 to 214 computations (42% saved)

series29.0ms (1.2%)

Error

0.9b

Counts

1 → 6

Calls

1 calls:

28.0ms

(/.f64 (atan2.f64 im re) (log.f64 10))

Compiler

Compiled 104 to 78 computations (25% saved)

simplify162.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

1288×	`associate-/l/_binary64`
677×	`unswap-sqr_binary64`
574×	`associate-/r/_binary64`
397×	`div-sub_binary64`
350×	`times-frac_binary64`

Counts

37 → 11

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	583
1	90	545
2	175	545
3	291	545
4	446	545
5	662	545
6	1661	545
7	2000	545
8	2327	545
9	3237	545
10	3312	545
11	3325	545
12	4310	545
13	4812	545
14	4782	545

prune11.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	8	3	11
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	8	4	12

Error

0.1b

Counts

12 → 4

Alt Table

Status	Error	Program
▶	1.9b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	5.9b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
	30.7b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))
✓	0.9b	(/.f64 (atan2.f64 im re) (log.f64 10))

Compiler

Compiled 158 to 91 computations (42.4% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.9b	(*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))
5.5b	(cbrt.f64 (atan2.f64 im re))
5.5b	(cbrt.f64 (atan2.f64 im re))
5.5b	(cbrt.f64 (atan2.f64 im re))

rewrite70.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))
1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 1603 to 425 computations (73.5% saved)

series145.0ms (5.7%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

41.0ms	(*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))
35.0ms	(cbrt.f64 (atan2.f64 im re))
33.0ms	(cbrt.f64 (atan2.f64 im re))
32.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 995 to 573 computations (42.4% saved)

simplify104.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

819×	`log-prod_binary64`
569×	`distribute-rgt-in_binary64`
530×	`distribute-lft-in_binary64`
455×	`unswap-sqr_binary64`
355×	`*-commutative_binary64`

Counts

97 → 78

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	49	1042
1	79	961
2	243	929
3	560	909
4	1392	731
5	3016	731
6	4211	731
7	4772	731

prune30.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	76	6	82

Error

0.1b

Counts

82 → 6

Alt Table

Status	Error	Program
✓	1.9b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	5.3b	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
▶	2.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 5) (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	5.9b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
	30.7b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))
✓	0.9b	(/.f64 (atan2.f64 im re) (log.f64 10))

Compiler

Compiled 678 to 304 computations (55.2% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 5)
5.5b	(cbrt.f64 (atan2.f64 im re))
5.5b	(cbrt.f64 (atan2.f64 im re))
5.5b	(cbrt.f64 (atan2.f64 im re))

rewrite66.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

18×	`cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow1/3_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`

Counts

4 → 57

Calls

4 calls:

3.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 5)
1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 1541 to 550 computations (64.3% saved)

series163.0ms (6.4%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

52.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 5)
36.0ms	(cbrt.f64 (atan2.f64 im re))
36.0ms	(cbrt.f64 (atan2.f64 im re))
34.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 1229 to 739 computations (39.9% saved)

simplify101.0ms (4%)

Algorithm

1×	egg-herbie

Rules

426×	`log-prod_binary64`
369×	`*-commutative_binary64`
358×	`associate-l_binary64`
332×	`sqr-pow_binary64`
327×	`associate-/l/_binary64`

Counts

81 → 53

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	61	927
1	108	861
2	211	861
3	486	861
4	1357	845
5	3041	833
6	4492	832
7	4745	832

prune31.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	51	8	59

Error

0.1b

Counts

59 → 8

Alt Table

Status	Error	Program
	32.5b	(.f64 (.f64 (cbrt.f64 (*.f64 (atan2.f64 im re) (pow.f64 (atan2.f64 im re) 2/3))) (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
✓	1.9b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	5.3b	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
✓	2.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 5) (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
▶	2.7b	(.f64 (.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 2)) 5) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))) 5)) (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	5.9b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
	30.7b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))
✓	0.9b	(/.f64 (atan2.f64 im re) (log.f64 10))

Compiler

Compiled 822 to 383 computations (53.4% saved)

localize21.0ms (0.8%)

Local error

Found 4 expressions with local error:

5.5b	(cbrt.f64 (atan2.f64 im re))
5.5b	(cbrt.f64 (atan2.f64 im re))
5.5b	(cbrt.f64 (atan2.f64 im re))
5.5b	(cbrt.f64 (atan2.f64 im re))

rewrite55.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

12×	`cbrt-prod_binary64`
8×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
4×	`pow1/3_binary64` `pow1_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 1702 to 660 computations (61.2% saved)

series160.0ms (6.3%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

40.0ms	(cbrt.f64 (atan2.f64 im re))
39.0ms	(cbrt.f64 (atan2.f64 im re))
38.0ms	(cbrt.f64 (atan2.f64 im re))
37.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 1866 to 1114 computations (40.3% saved)

simplify96.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

813×	`associate-/r/_binary64`
618×	`log-prod_binary64`
449×	`associate-l_binary64`
350×	`distribute-rgt-out_binary64`
295×	`associate-r_binary64`

Counts

68 → 44

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	580
1	27	552
2	54	552
3	112	552
4	344	536
5	1538	536
6	2826	536
7	3718	536
8	5193	536

prune25.0ms (1%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	43	9	52

Error

0.1b

Counts

52 → 9

Alt Table

Status	Error	Program
	31.4b	(.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 2)) 5) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2/3)) (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))))) 5)) (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	32.5b	(.f64 (.f64 (cbrt.f64 (*.f64 (atan2.f64 im re) (pow.f64 (atan2.f64 im re) 2/3))) (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	1.9b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	5.3b	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	2.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 5) (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	2.7b	(.f64 (.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 2)) 5) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))) 5)) (cbrt.f64 (cbrt.f64 (atan2.f64 im re)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	5.9b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
	30.7b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))
	0.9b	(/.f64 (atan2.f64 im re) (log.f64 10))

Compiler

Compiled 694 to 343 computations (50.6% saved)

regimes402.0ms (15.8%)

Accuracy

Total 0.8b remaining (90.6%)

Threshold costs 0.8b (90.6%)

Compiler

Compiled 7514 to 3989 computations (46.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64` `*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	14	21
2	13	21

end1.0ms (0%)

Compiler: Compiled 15 to 13 computations (13.3% saved)

sample757.0ms (29.8%)

Algorithm

1×

intervals

Results

314.0ms

8000×

body

128

valid

Compiler

Compiled 221 to 134 computations (39.4% saved)

Details

analyze21.0ms (0.8%)

sample18.0ms (0.7%)

simplify7.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite34.0ms (1.3%)

series29.0ms (1.2%)

simplify162.0ms (6.4%)

prune11.0ms (0.4%)

localize9.0ms (0.4%)

rewrite70.0ms (2.8%)

series145.0ms (5.7%)

simplify104.0ms (4.1%)

prune30.0ms (1.2%)

localize13.0ms (0.5%)

rewrite66.0ms (2.6%)

series163.0ms (6.4%)

simplify101.0ms (4%)

prune31.0ms (1.2%)

localize21.0ms (0.8%)

rewrite55.0ms (2.1%)

series160.0ms (6.3%)

simplify96.0ms (3.8%)

prune25.0ms (1%)

regimes402.0ms (15.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample757.0ms (29.8%)

Profiling