Details

analyze4.0ms (0.2%)

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)

sample698.0ms (29.4%)

Infinites

0% of outputs are infinite.

Results

652.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

prune2.0ms (0.1%)

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 (0.2%)

Local error

Found 1 expressions with local error:

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

series57.0ms (2.4%)

Counts

1 → 0

Calls

1 calls:

57.0ms

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

rewrite4.0ms (0.2%)

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))

simplify111.0ms (4.7%)

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

prune29.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	23	9	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	9	33

Error

0.0b

Counts

33 → 9

Alt Table

Status	Error	Program
	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))))
	30.9b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (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))))
	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)))
	30.5b	(*.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))))
	7.5b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
▶	0.7b	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))

Compiler

Compiled 719 to 437 computations (39.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
✓	0.6b	(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))
	0.8b	(/.f64 (atan2.f64 im re) (log.f64 10))

series104.0ms (4.4%)

Counts

2 → 48

Calls

2 calls:

53.0ms	(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))
51.0ms	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))
0.0ms	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))

simplify72.0ms (3%)

Algorithm

1×	egg-herbie

Rules

932×	`unsub-neg_binary64`
460×	`distribute-neg-out_binary64`
355×	`distribute-rgt-in_binary64`
295×	`distribute-lft-in_binary64`
290×	`sub-neg_binary64`

Counts

70 → 30

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	786
1	36	744
2	75	744
3	141	744
4	408	744
5	1794	744
6	3396	744
7	5040	744

prune42.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	62	9	71

Error

0.0b

Counts

71 → 9

Alt Table

Status	Error	Program
	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))))
	30.9b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (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))))
	0.8b	(log1p.f64 (.f64 (.f64 (cbrt.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))) (cbrt.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))) (cbrt.f64 (expm1.f64 (/.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)))
	30.5b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	7.5b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
✓	0.7b	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))

Compiler

Compiled 1170 to 761 computations (35% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))
✓	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))

series106.0ms (4.5%)

Counts

2 → 48

Calls

2 calls:

58.0ms	(/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))
48.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))

rewrite34.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
85×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
51×	`sqrt-prod_binary64`
46×	`add-cube-cbrt_binary64`

Counts

2 → 136

Calls

2 calls:

17.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
3.0ms	(/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))

simplify245.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-neg_binary64`
413×	`div-sub_binary64`
411×	`associate-/l*_binary64`
410×	`*-commutative_binary64`
326×	`sqr-pow_binary64`

Counts

184 → 158

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	132	3954
1	293	3396
2	887	3396
3	1945	3064
4	2127	3016
5	2461	3016
6	3273	3016
7	4164	3016
8	4684	2992
9	4970	2992
10	4687	2992

prune126.0ms (5.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	159	8	167

Error

0.0b

Counts

167 → 8

Alt Table

Status	Error	Program
	7.5b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 (.f64 (.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (.f64 (*.f64 (sqrt.f64 (log.f64 10)) (sqrt.f64 (log.f64 10))) (sqrt.f64 (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)))
▶	0.8b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
	30.5b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	1.0b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (*.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))) (cbrt.f64 (/.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))))
	0.8b	(log1p.f64 (.f64 (.f64 (cbrt.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))) (cbrt.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))) (cbrt.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))))
✓	0.7b	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))

Compiler

Compiled 3854 to 2896 computations (24.9% saved)

localize13.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10))))
✓	0.8b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
✓	1.0b	(/.f64 1 (log.f64 10))

series104.0ms (4.4%)

Counts

3 → 24

Calls

3 calls:

54.0ms	(*.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10))))
49.0ms	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
0.0ms	(/.f64 1 (log.f64 10))

rewrite31.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`times-frac_binary64`
45×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
31×	`sqrt-prod_binary64`

Counts

3 → 130

Calls

3 calls:

11.0ms	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
7.0ms	(*.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10))))
2.0ms	(/.f64 1 (log.f64 10))

simplify184.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-def_binary64`
664×	`fabs-mul_binary64`
562×	`pow-sqr_binary64`
512×	`associate-/l/_binary64`
420×	`fma-neg_binary64`

Counts

154 → 163

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	121	2422
1	232	2177
2	672	2177
3	1381	1820
4	1601	1820
5	1819	1820
6	2233	1820
7	3083	1814
8	3992	1814
9	4454	1814
10	4922	1814
11	5022	1814

prune106.0ms (4.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	6	0	6
Picked	0	1	1
Done	0	1	1
Total	168	3	171

Error

0.0b

Counts

171 → 3

Alt Table

Status	Error	Program
	0.1b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2)))
✓	0.8b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
✓	0.7b	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))

Compiler

Compiled 3562 to 2935 computations (17.6% saved)

regimes189.0ms (8%)

Accuracy

Total 0.1b remaining (87.9%)

Threshold costs 0.1b (87.9%)

Counts

42 → 1

Compiler

Compiled 3946 to 3051 computations (22.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	29
1	20	29
2	19	29

end78.0ms (3.3%)

Compiler: Compiled 87 to 77 computations (11.5% saved)

Details

analyze4.0ms (0.2%)

sample698.0ms (29.4%)

simplify6.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series57.0ms (2.4%)

rewrite4.0ms (0.2%)

simplify111.0ms (4.7%)

prune29.0ms (1.2%)

localize8.0ms (0.3%)

series104.0ms (4.4%)

rewrite1.0ms (0.1%)

simplify72.0ms (3%)

prune42.0ms (1.8%)

localize10.0ms (0.4%)

series106.0ms (4.5%)

rewrite34.0ms (1.4%)

simplify245.0ms (10.3%)

prune126.0ms (5.3%)

localize13.0ms (0.5%)

series104.0ms (4.4%)

rewrite31.0ms (1.3%)

simplify184.0ms (7.8%)

prune106.0ms (4.4%)

regimes189.0ms (8%)

simplify2.0ms (0.1%)

end78.0ms (3.3%)

Profiling