Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	197×	body	80	valid
3.0ms	20×	body	1280	valid
3.0ms	16×	body	2560	valid
2.0ms	10×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	5×	body	640	valid
0.0ms	1×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Merged error: 35.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
5×	`add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `diff-log` `pow-prod-down` `sum-log` `distribute-lft-out--`

Counts

4 → 54

Calls

4 calls:

7.0ms	(+ (* re re) (* im im))
7.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
185.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
68.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	258	459
1	938	422
2	3098	412
3	5001	410

prune185.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	5	67

Merged error: 16.4b

Counts

67 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
5.2b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
21.0b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
13.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
206.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
71.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	417	1078
1	1461	985
2	5001	978

prune298.0ms

Filtered

111 candidates to 77 candidates (69.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	107	9	116

Merged error: 6.1b

Counts

116 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
5.2b	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`associate-r`
14×	`add-cube-cbrt`
13×	`pow1` `times-frac`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`sqrt-pow1` `pow-prod-down` `sqrt-prod` `distribute-lft-out`
3×	`flip3-+` `sqrt-div` `associate-r/` `associate-l*` `flip-+`
2×	`pow1/2` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `div-exp` `sum-log` `*-commutative` `div-inv`

Counts

4 → 77

Calls

4 calls:

16.0ms	(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
170.0ms	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	463	834
1	2015	732
2	5001	726

prune284.0ms

Filtered

89 candidates to 70 candidates (78.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	90	8	98

Merged error: 5.2b

Counts

98 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

5.2b	(sqrt (* 2.0 (* (* (fabs im) (/ (* (cbrt (fabs im)) (cbrt (fabs im))) (* (cbrt (+ (sqrt (+ (* re re) (* im im))) re)) (cbrt (+ (sqrt (+ (* re re) (* im im))) re))))) (/ (cbrt (fabs im)) (cbrt (+ (sqrt (+ (* re re) (* im im))) re))))))
27.5b	(sqrt (+ (* re re) (* im im)))
27.5b	(sqrt (+ (* re re) (* im im)))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
10×	`add-sqr-sqrt` `sqrt-prod`
9×	`sqrt-div`
7×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`associate-*r/` `pow-prod-down`
4×	`add-exp-log` `pow1/2` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`frac-times` `associate-*l/`

Counts

4 → 61

Calls

4 calls:

37.0ms	(sqrt (* 2.0 (* (* (fabs im) (/ (* (cbrt (fabs im)) (cbrt (fabs im))) (* (cbrt (+ (sqrt (+ (* re re) (* im im))) re)) (cbrt (+ (sqrt (+ (* re re) (* im im))) re))))) (/ (cbrt (fabs im)) (cbrt (+ (sqrt (+ (* re re) (* im im))) re))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(sqrt (* 2.0 (* (* (fabs im) (/ (* (cbrt (fabs im)) (cbrt (fabs im))) (* (cbrt (+ (sqrt (+ (* re re) (* im im))) re)) (cbrt (+ (sqrt (+ (* re re) (* im im))) re))))) (/ (cbrt (fabs im)) (cbrt (+ (sqrt (+ (* re re) (* im im))) re))))))
37.0ms	(sqrt (+ (* re re) (* im im)))
43.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify133.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	300	802
1	1062	750
2	4528	741
3	5001	725

prune323.0ms

Filtered

73 candidates to 60 candidates (82.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	73	8	81

Merged error: 5.2b

Counts

81 → 8

regimes211.0ms

Accuracy

48% (18.2b remaining)

Error of 23.6b against oracle of 5.4b and baseline of 40.4b

bsearch242.0ms

Steps

Iters	Range		Point
4	1.5549168953101855e+143	2.483185623213712e+143	1.7411669279487403e+143
8	2.033804478772488e-16	1.0574984813846425e-13	2.5127945524088855e-16
6	4.047275585948234e-45	4.151680347800628e-44	3.614486343345858e-44
6	1.6552168713535222e-160	7.56737574009597e-160	5.737581771432969e-160
9	-1.7961890248789646e-153	-4.991866581371744e-162	-6.997538802703971e-155
8	-1.8924915151658963e+19	-8893382635004147.0	-4.2621787475413843e+17

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	58
1	82	58
2	83	58
3	83	58

end0.0ms

sample687.0ms

Algorithm

intervals

Results

204.0ms	6006×	body	80	valid
147.0ms	717×	body	2560	valid
78.0ms	481×	body	1280	valid
69.0ms	280×	body	5120	valid
37.0ms	273×	body	640	valid
14.0ms	147×	body	320	valid
6.0ms	96×	body	160	valid