Details

analyze4.0ms (0.1%)

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)

sample773.0ms (11.1%)

Results

740.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

prune2.0ms (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

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (atan2.f64 im re) (log.f64 10))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 (atan2.f64 im re) (log.f64 10))

series54.0ms (0.8%)

Counts

1 → 0

Calls

1 calls:

54.0ms

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`

Counts

1 → 33

Calls

1 calls:

2.0ms

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

simplify117.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1288×	`associate-/l/_binary64`
1067×	`fma-neg_binary64`
979×	`fma-def_binary64`
677×	`unswap-sqr_binary64`
350×	`times-frac_binary64`

Counts

33 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	551
1	92	513
2	177	513
3	294	513
4	454	513
5	676	513
6	1686	513
7	2393	513
8	2851	513
9	3810	513
10	4033	513
11	4008	513
12	4982	513

prune33.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	25	7	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	7	33

Error

0.0b

Counts

33 → 7

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)))
	33.2b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	5.3b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
▶	0.8b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
	2.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (sqrt.f64 (log.f64 10))))

Compiler

Compiled 671 to 405 computations (39.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
✓	0.8b	(/.f64 (log.f64 10) (atan2.f64 im re))

series104.0ms (1.5%)

Counts

2 → 24

Calls

2 calls:

56.0ms	(/.f64 (log.f64 10) (atan2.f64 im re))
48.0ms	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

2 → 123

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
3.0ms	(/.f64 (log.f64 10) (atan2.f64 im re))

simplify207.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1150×	`fabs-mul_binary64`
912×	`fma-def_binary64`
471×	`unswap-sqr_binary64`
448×	`fma-neg_binary64`
383×	`associate-/l/_binary64`

Counts

147 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	2599
1	169	2355
2	393	2318
3	784	2318
4	1045	2318
5	1138	2318
6	1485	2318
7	1880	2318
8	2301	2318
9	3347	2318
10	4650	2318
11	4689	2318
12	4946	2318

prune125.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	135	10	145

Error

0.0b

Counts

145 → 10

Alt Table

Status	Error	Program
	33.6b	(/.f64 (/.f64 1 (/.f64 (sqrt.f64 (log.f64 10)) (sqrt.f64 (atan2.f64 im re)))) (/.f64 (sqrt.f64 (log.f64 10)) (sqrt.f64 (atan2.f64 im re))))
	0.8b	(/.f64 1 (*.f64 (log.f64 10) (/.f64 1 (atan2.f64 im re))))
	2.2b	(/.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))) (/.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (atan2.f64 im re))))
	5.8b	(/.f64 1 (cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 10) (log.f64 10)) (log.f64 10)) (.f64 (.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)))))
	2.1b	(.f64 (/.f64 1 (/.f64 (sqrt.f64 (log.f64 10)) (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))))) (/.f64 1 (/.f64 (sqrt.f64 (log.f64 10)) (cbrt.f64 (atan2.f64 im re)))))
▶	0.7b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	5.3b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (/.f64 (log.f64 10) (atan2.f64 im re)) (/.f64 (log.f64 10) (atan2.f64 im re))) (/.f64 (log.f64 10) (atan2.f64 im re)))))
	0.8b	(/.f64 1 (/.f64 1 (/.f64 (atan2.f64 im re) (log.f64 10))))
	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))

Compiler

Compiled 2814 to 1849 computations (34.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))
✓	0.1b	(*.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))
	0.8b	(/.f64 (log.f64 10) (atan2.f64 im re))
✓	4.4b	(cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))

series2.2s (31%)

Counts

3 → 72

Calls

3 calls:

1.4s

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

730.0ms

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

60.0ms

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

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`cbrt-prod_binary64`
91×	`times-frac_binary64`
88×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
60×	`add-cube-cbrt_binary64`

Counts

3 → 181

Calls

3 calls:

15.0ms

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

14.0ms

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

2.0ms

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

simplify184.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

753×	`unswap-sqr_binary64`
643×	`fma-def_binary64`
350×	`*-commutative_binary64`
292×	`times-frac_binary64`
226×	`associate-/l*_binary64`

Counts

253 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	6002
1	274	5311
2	990	5028
3	2277	4918
4	4460	4918
5	5004	4918

prune397.0ms (5.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	366	5	371
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	369	12	381

Error

Counts

381 → 12

Alt Table

Status	Error	Program
	5.7b	(/.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 10) (atan2.f64 im re)) (/.f64 (log.f64 10) (atan2.f64 im re))) (/.f64 (log.f64 10) (atan2.f64 im re)))))
	5.3b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (/.f64 (log.f64 10) (atan2.f64 im re)) (/.f64 (log.f64 10) (atan2.f64 im re))) (/.f64 (log.f64 10) (atan2.f64 im re)))))
▶	0.5b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))))
	0.8b	(/.f64 1 (/.f64 1 (/.f64 (atan2.f64 im re) (log.f64 10))))
	2.1b	(.f64 (/.f64 1 (/.f64 (sqrt.f64 (log.f64 10)) (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))))) (/.f64 1 (/.f64 (sqrt.f64 (log.f64 10)) (cbrt.f64 (atan2.f64 im re)))))
✓	0.7b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	1.1b	(/.f64 1 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10)))) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (log.f64 10)) (atan2.f64 im re))) (cbrt.f64 (/.f64 (sqrt.f64 (log.f64 10)) (atan2.f64 im re))))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	4.6b	(/.f64 1 (.f64 (cbrt.f64 (.f64 (/.f64 (log.f64 10) (atan2.f64 im re)) (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	0.8b	(/.f64 1 (pow.f64 (/.f64 (log.f64 10) (atan2.f64 im re)) 1))
	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
	2.2b	(/.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))) (/.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (atan2.f64 im re))))

Compiler

Compiled 12693 to 8274 computations (34.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))
	0.8b	(/.f64 (log.f64 10) (atan2.f64 im re))
✓	4.4b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	4.4b	(cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))

series710.0ms (10.2%)

Counts

1 → 24

Calls

1 calls:

710.0ms

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

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`cbrt-div_binary64`
5×	`associate-*l/_binary64`
5×	`frac-times_binary64`
3×	`associate-*r/_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 19

Calls

1 calls:

12.0ms

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

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

812×	`unswap-sqr_binary64`
353×	`distribute-rgt-in_binary64`
349×	`distribute-lft-in_binary64`
322×	`log-prod_binary64`
312×	`fma-neg_binary64`

Counts

43 → 30

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	48	694
1	50	646
2	109	644
3	267	644
4	763	602
5	2683	602
6	4880	602
7	4963	602

prune894.0ms (12.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	564	0	564
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	564	12	576

Error

Counts

576 → 12

Alt Table

Status	Error	Program
	5.7b	(/.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 10) (atan2.f64 im re)) (/.f64 (log.f64 10) (atan2.f64 im re))) (/.f64 (log.f64 10) (atan2.f64 im re)))))
	5.3b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (/.f64 (log.f64 10) (atan2.f64 im re)) (/.f64 (log.f64 10) (atan2.f64 im re))) (/.f64 (log.f64 10) (atan2.f64 im re)))))
✓	0.5b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))))
	0.8b	(/.f64 1 (/.f64 1 (/.f64 (atan2.f64 im re) (log.f64 10))))
	2.1b	(.f64 (/.f64 1 (/.f64 (sqrt.f64 (log.f64 10)) (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))))) (/.f64 1 (/.f64 (sqrt.f64 (log.f64 10)) (cbrt.f64 (atan2.f64 im re)))))
✓	0.7b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	1.1b	(/.f64 1 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10)))) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (log.f64 10)) (atan2.f64 im re))) (cbrt.f64 (/.f64 (sqrt.f64 (log.f64 10)) (atan2.f64 im re))))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	4.6b	(/.f64 1 (.f64 (cbrt.f64 (.f64 (/.f64 (log.f64 10) (atan2.f64 im re)) (/.f64 (log.f64 10) (atan2.f64 im re)))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	0.8b	(/.f64 1 (pow.f64 (/.f64 (log.f64 10) (atan2.f64 im re)) 1))
	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
	2.2b	(/.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))) (/.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (atan2.f64 im re))))

Compiler

Compiled 28779 to 18680 computations (35.1% saved)

regimes720.0ms (10.3%)

Accuracy

Total 0.7b remaining (94.6%)

Threshold costs 0.7b (94.6%)

Counts

133 → 1

Compiler

Compiled 12608 to 9171 computations (27.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	58
1	21	58
2	19	58

end298.0ms (4.3%)

Compiler: Compiled 386 to 276 computations (28.5% saved)

Details

analyze4.0ms (0.1%)

sample773.0ms (11.1%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series54.0ms (0.8%)

rewrite4.0ms (0.1%)

simplify117.0ms (1.7%)

prune33.0ms (0.5%)

localize6.0ms (0.1%)

series104.0ms (1.5%)

rewrite17.0ms (0.2%)

simplify207.0ms (3%)

prune125.0ms (1.8%)

localize13.0ms (0.2%)

series2.2s (31%)

rewrite52.0ms (0.7%)

simplify184.0ms (2.6%)

prune397.0ms (5.7%)

localize13.0ms (0.2%)

series710.0ms (10.2%)

rewrite14.0ms (0.2%)

simplify76.0ms (1.1%)

prune894.0ms (12.8%)

regimes720.0ms (10.3%)

simplify3.0ms (0%)

end298.0ms (4.3%)

Profiling