Details

sample50.0ms

Algorithm

intervals

Results

12.0ms	182×	body	80	valid
9.0ms	22×	body	1280	valid
8.0ms	21×	body	2560	valid
7.0ms	15×	body	5120	valid
2.0ms	10×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

11.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
18.0ms	(- (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series34.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	232	382
1	768	356
2	2506	346
3	5001	344

prune414.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
6.5b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
20.2b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite55.0ms

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:

13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
15.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
20.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
21.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	417	1094
1	1519	985
2	5002	975

prune871.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
6.5b	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite96.0ms

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:

42.0ms	(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
14.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
33.0ms	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
3.0ms	(sqrt (+ (* re re) (* im im)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
28.0ms	(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (47.0ms)

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

prune824.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize18.0ms

Local error

Found 4 expressions with local error:

5.2b	(sqrt (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
6.5b	(sqrt (* 2.0 (* (* (sqrt (fabs im)) (sqrt (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))) (* (sqrt (fabs im)) (sqrt (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))))
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1`
25×	`sqrt-prod`
20×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
13×	`times-frac` `pow-prod-down`
12×	`sqrt-div`
9×	`sqrt-pow1`
8×	`associate-*r/`
4×	`add-exp-log` `rem-sqrt-square` `pow1/2` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `distribute-lft-out`
2×	`associate-/r/`
1×	`frac-times` `associate-*l/` `div-inv`

Counts

4 → 78

Calls

4 calls:

20.0ms	(sqrt (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
285.0ms	(sqrt (* 2.0 (* (* (sqrt (fabs im)) (sqrt (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))) (* (sqrt (fabs im)) (sqrt (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
26.0ms	(sqrt (* 2.0 (* (* (sqrt (fabs im)) (sqrt (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))) (* (sqrt (fabs im)) (sqrt (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	496	1049
1	1940	980
2	5002	970

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.8b

regimes392.0ms

Accuracy

52% (16.8b remaining)

Error of 19.8b against oracle of 3.1b and baseline of 38.0b

bsearch93.0ms

Steps

Iters	Range		Point
7	2.3676647091815954e+142	5.462432632406119e+143	5.394476249583853e+143
5	-8.482171429905235e-305	-3.7894152148416054e-305	-8.055586096901738e-305
7	-3.0066066471288133e-266	-7.005394620018514e-268	-7.36720432236372e-267
7	-4.2189696159604594e+122	-1.4140661128715776e+121	-2.463228932581569e+122

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	53
1	80	53
2	81	53
3	81	53

end0.0ms

sample1.2s

Algorithm

intervals

Results

378.0ms	6023×	body	80	valid
262.0ms	681×	body	2560	valid
149.0ms	487×	body	1280	valid
134.0ms	303×	body	5120	valid
67.0ms	281×	body	640	valid
27.0ms	151×	body	320	valid
9.0ms	74×	body	160	valid