Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	207×	body	80	valid
4.0ms	18×	body	2560	valid
3.0ms	10×	body	5120	valid
2.0ms	13×	body	1280	valid
1.0ms	5×	body	640	valid
0.0ms	2×	body	320	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

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:

12.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
18.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (70.0ms)

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

prune142.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
5.2b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
23.4b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

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:

14.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
13.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
23.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
192.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
66.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (39.0ms)

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

prune288.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
30.4b	(sqrt (* 2.0 (pow im 2)))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
32×	`sqrt-prod`
28×	`times-frac`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
7×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`sqrt-div` `associate-/l*`
3×	`flip3-+` `flip-+`
2×	`sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

22.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
16.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
2.0ms	(sqrt (* 2.0 (pow im 2)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (* 2.0 (pow im 2)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	387	1210
1	1325	1133
2	5002	1103

prune311.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2.0) (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (fabs im))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `times-frac` `associate-/r*`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div`
3×	`flip3-+` `associate-r` `flip-+` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `sum-log` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

24.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(* (sqrt 2.0) (fabs im))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
37.0ms	(* (sqrt 2.0) (fabs im))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	433	806
1	1901	727
2	5001	716

prune254.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.9b

regimes149.0ms

Accuracy

35.3% (23.9b remaining)

Error of 24.4b against oracle of 0.6b and baseline of 37.4b

bsearch221.0ms

Steps

Iters	Range		Point
5	1.4215696808062822e-115	4.675966861882339e-115	1.4493474230643574e-115
8	-1.3229972502418326e-211	-8.43775892024765e-215	-4.1831474358645474e-212
8	-2.5946119843782734e-200	-2.9755272848592795e-204	-3.0163934746462264e-204
8	-5.775474684297679e-138	-1.8431099240066617e-140	-1.9966008063578885e-140
9	-3.827552672707701e+33	-7.814960403485421e+27	-2.504931184133823e+32

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	35
1	72	35
2	73	35
3	73	35

end0.0ms

sample695.0ms

Algorithm

intervals

Results

215.0ms	6096×	body	80	valid
130.0ms	637×	body	2560	valid
77.0ms	443×	body	1280	valid
72.0ms	296×	body	5120	valid
39.0ms	303×	body	640	valid
14.0ms	146×	body	320	valid
5.0ms	79×	body	160	valid