Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	181×	body	80	valid
5.0ms	26×	body	2560	valid
3.0ms	17×	body	1280	valid
2.0ms	17×	body	640	valid
2.0ms	8×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

15.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series271.0ms

Counts

3 → 9

Calls

3 calls:

183.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	244	351
1	743	325
2	2278	315
3	5001	312

prune335.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.3b

localize17.0ms

Local error

Found 4 expressions with local error:

13.1b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 56

Calls

4 calls:

36.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	160	641
1	431	527
2	1354	481
3	5001	477

prune247.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.3b

localize18.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
30.5b	(cbrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 58

Calls

4 calls:

3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	141	422
1	440	404
2	1469	402
3	5002	399

prune299.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.3b

localize22.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
30.5b	(cbrt (+ (* re re) (* im im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 58

Calls

4 calls:

3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	141	422
1	440	404
2	1469	402
3	5002	399

prune334.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.3b

regimes158.0ms

Accuracy

58.3% (8.8b remaining)

Error of 27.0b against oracle of 18.2b and baseline of 39.3b

bsearch105.0ms

Steps

Iters	Range		Point
8	3.043105375567236e+91	2.6176408404764512e+94	3.7988918544800208e+93
10	1.8336546264510258e-269	2.4399585913960157e-258	2.0796209369763628e-269

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	48
1	47	48

end0.0ms

sample686.0ms

Algorithm

intervals

Results

205.0ms	6015×	body	80	valid
141.0ms	695×	body	2560	valid
84.0ms	500×	body	1280	valid
68.0ms	285×	body	5120	valid
37.0ms	292×	body	640	valid
13.0ms	137×	body	320	valid
5.0ms	76×	body	160	valid