Details

Time bar (total: 17.8s)

sample63.0ms

Algorithm
intervals
Results
21.0ms193×body80valid
13.0ms25×body2560valid
6.0ms11×body5120valid
6.0ms14×body1280valid
2.0ms7×body640valid
1.0ms5×body320valid
0.0ms1×body160valid

simplify41.0ms

Counts
1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize43.0ms

Local error

Found 3 expressions with local error:

31.2b
(sqrt (+ (* re re) (* im im)))
0.2b
(+ (sqrt (+ (* re re) (* im im))) re)
0.0b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×*-un-lft-identity
5×add-sqr-sqrt add-log-exp
4×sqrt-div add-cube-cbrt sqrt-prod
3×sqrt-pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square sum-log pow-prod-down distribute-lft-out
Counts
3 → 43
Calls
3 calls:
Slowest
35.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
18.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms
(sqrt (+ (* re re) (* im im)))

series367.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
257.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
59.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
50.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts
52 → 52

prune601.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.5b

localize65.0ms

Local error

Found 4 expressions with local error:

31.2b
(sqrt (+ (* re re) (* im im)))
30.6b
(sqrt (* 2.0 (- (* im im) 0)))
0.3b
(/ (sqrt (* 2.0 (- (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.3b
(- (sqrt (+ (* re re) (* im im))) re)

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt sqrt-prod
37×*-un-lft-identity
36×times-frac
25×add-cube-cbrt
12×difference-of-squares
9×associate-/r*
8×pow1 sqrt-div
6×add-cbrt-cube add-exp-log distribute-lft-out-- add-log-exp
4×flip3-- associate-*r/ insert-posit16 flip-- associate-/l*
3×sqrt-pow1
2×pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv rem-sqrt-square sqrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-exp pow-prod-down flip-+ div-inv
Counts
4 → 113
Calls
4 calls:
Slowest
47.0ms
(/ (sqrt (* 2.0 (- (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
46.0ms
(- (sqrt (+ (* re re) (* im im))) re)
19.0ms
(sqrt (* 2.0 (- (* im im) 0)))
12.0ms
(sqrt (+ (* re re) (* im im)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
287.0ms
(/ (sqrt (* 2.0 (- (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
71.0ms
(sqrt (+ (* re re) (* im im)))
61.0ms
(- (sqrt (+ (* re re) (* im im))) re)
45.0ms
(sqrt (* 2.0 (- (* im im) 0)))

simplify1.3s

Counts
125 → 125

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.0b

localize60.0ms

Local error

Found 4 expressions with local error:

31.2b
(sqrt (+ (* re re) (* im im)))
0.4b
(* (sqrt 2.0) (fabs im))
0.3b
(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.3b
(- (sqrt (+ (* re re) (* im im))) re)

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×sqrt-prod
18×*-un-lft-identity
12×add-cube-cbrt
11×add-cbrt-cube add-exp-log
9×associate-/r* times-frac
7×pow1
6×associate-*l* add-log-exp difference-of-squares
4×sqrt-div insert-posit16
3×associate-*r* distribute-lft-out--
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod flip-- unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log pow-prod-down *-commutative flip-+ div-inv associate-/l*
Counts
4 → 91
Calls
4 calls:
Slowest
69.0ms
(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
58.0ms
(- (sqrt (+ (* re re) (* im im))) re)
15.0ms
(* (sqrt 2.0) (fabs im))
12.0ms
(sqrt (+ (* re re) (* im im)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
235.0ms
(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
81.0ms
(- (sqrt (+ (* re re) (* im im))) re)
63.0ms
(sqrt (+ (* re re) (* im im)))
47.0ms
(* (sqrt 2.0) (fabs im))

simplify2.3s

Counts
103 → 103

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize51.0ms

Local error

Found 4 expressions with local error:

31.2b
(sqrt (+ (* re re) (* im im)))
0.5b
(* (sqrt 2.0) (sqrt (fabs im)))
0.3b
(* (* (sqrt 2.0) (sqrt (fabs im))) (sqrt (fabs im)))
0.3b
(/ (* (* (sqrt 2.0) (sqrt (fabs im))) (sqrt (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
30×sqrt-prod
20×add-cbrt-cube add-exp-log
19×*-un-lft-identity
17×pow1
15×add-cube-cbrt
12×associate-*r*
10×pow-prod-down
9×associate-/r* times-frac
7×associate-*l* prod-exp cbrt-unprod
6×sqrt-pow1 pow1/2
5×sqrt-unprod
4×sqrt-div insert-posit16 add-log-exp difference-of-squares unswap-sqr
3×cbrt-undiv div-exp
2×associate-/r/ *-commutative distribute-lft-out--
1×rem-sqrt-square sqrt-undiv clear-num frac-2neg flip3-+ flip3-- flip-+ div-inv flip-- associate-/l*
Counts
4 → 111
Calls
4 calls:
Slowest
64.0ms
(/ (* (* (sqrt 2.0) (sqrt (fabs im))) (sqrt (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
35.0ms
(* (* (sqrt 2.0) (sqrt (fabs im))) (sqrt (fabs im)))
11.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(* (sqrt 2.0) (sqrt (fabs im)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
264.0ms
(/ (* (* (sqrt 2.0) (sqrt (fabs im))) (sqrt (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
66.0ms
(* (sqrt 2.0) (sqrt (fabs im)))
60.0ms
(sqrt (+ (* re re) (* im im)))
54.0ms
(* (* (sqrt 2.0) (sqrt (fabs im))) (sqrt (fabs im)))

simplify1.3s

Counts
123 → 123

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

regimes592.0ms

Accuracy

65.4% (10.3b remaining)

Error of 17.8b against oracle of 7.6b and baseline of 37.3b

bsearch371.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
864.0ms706×body2560valid
821.0ms6041×body80valid
292.0ms476×body1280valid
214.0ms266×body5120valid
112.0ms278×body640valid
41.0ms140×body320valid
18.0ms93×body160valid