Details

Time bar (total: 22.2s)

sample158.0ms

Algorithm
intervals
Results
20.0ms27×body2560valid
18.0ms185×body80valid
13.0ms22×body1280valid
9.0ms11×body5120valid
5.0ms8×body640valid
0.0ms1×body320valid
0.0ms2×body160valid

simplify127.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
127.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.7b
(- (hypot re im) re)
0.3b
(sqrt (* (- (hypot re im) re) 2.0))
0.0b
(hypot re im)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×prod-diff
6×pow1
5×add-log-exp
3×expm1-log1p-u add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
2×sqrt-pow1 flip3-- sqrt-div associate-*l/ flip--
1×hypot-udef sub-neg pow1/2 diff-log pow-prod-down sqrt-prod distribute-lft-out-- difference-of-squares
Counts
3 → 56
Calls
3 calls:
Slowest
8.0ms
(sqrt (* (- (hypot re im) re) 2.0))
6.0ms
(- (hypot re im) re)
1.0ms
(hypot re im)

series579.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
408.0ms
(sqrt (* (- (hypot re im) re) 2.0))
92.0ms
(hypot re im)
79.0ms
(- (hypot re im) re)

simplify1.0s

Counts
38 → 65
Calls
38 calls:
Slowest
263.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
112.0ms
(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
103.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
55.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* re 1)))
41.0ms
(fma 1 (hypot re im) (- (* (sqrt re) (sqrt re))))

prune563.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.6b

localize22.0ms

Local error

Found 3 expressions with local error:

0.7b
(- (hypot re im) re)
0.3b
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
0.0b
(hypot re im)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
18×*-un-lft-identity
14×add-cube-cbrt
12×sqrt-prod
9×prod-diff
8×associate-*l*
7×pow1
6×associate-*r*
5×add-cbrt-cube add-exp-log add-log-exp
4×unswap-sqr
3×expm1-log1p-u fma-neg pow-prod-down insert-posit16 log1p-expm1-u
2×sqrt-pow1 flip3-- pow1/2 sqrt-div associate-*l/ flip-- distribute-lft-out-- difference-of-squares
1×hypot-udef sub-neg sqrt-unprod diff-log prod-exp *-commutative cbrt-unprod
Counts
3 → 77
Calls
3 calls:
Slowest
16.0ms
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
10.0ms
(- (hypot re im) re)
0.0ms
(hypot re im)

series394.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
248.0ms
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
84.0ms
(- (hypot re im) re)
61.0ms
(hypot re im)

simplify1.5s

Counts
63 → 86
Calls
63 calls:
Slowest
310.0ms
(* (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) (sqrt (- (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
255.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt 2.0))
157.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))
58.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
44.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (sqrt re) (sqrt re))))

prune911.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (hypot re im) re)
0.3b
(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.2b
(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
0.0b
(hypot re im)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
32×sqrt-prod
23×*-un-lft-identity
19×add-cube-cbrt
18×associate-*r*
16×pow1
11×add-cbrt-cube add-exp-log
10×pow-prod-down
9×associate-*l* prod-diff
6×associate-*l/ add-log-exp unswap-sqr
5×sqrt-pow1 pow1/2
4×expm1-log1p-u sqrt-div prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×flip3-- fma-neg sqrt-unprod flip--
2×*-commutative distribute-lft-out-- difference-of-squares
1×hypot-udef sub-neg diff-log
Counts
4 → 114
Calls
4 calls:
Slowest
63.0ms
(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
28.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
10.0ms
(- (hypot re im) re)
0.0ms
(hypot re im)

series756.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
368.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
241.0ms
(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
76.0ms
(- (hypot re im) re)
70.0ms
(hypot re im)

simplify3.6s

Counts
95 → 126
Calls
95 calls:
Slowest
511.0ms
(* (* (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) (sqrt (- (hypot re im) re))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
302.0ms
(* (* (* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))) (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
256.0ms
(* (* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
241.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (sqrt 2.0)))
216.0ms
(* (* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.6b

localize53.0ms

Local error

Found 4 expressions with local error:

9.8b
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.3b
(* (* (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.2b
(* (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)) (sqrt (sqrt 2.0)))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
49×sqrt-prod
47×add-sqr-sqrt
31×pow1
24×associate-*r*
21×*-un-lft-identity add-cube-cbrt
14×associate-*l*
13×sqrt-pow1 add-cbrt-cube pow1/2 pow-prod-down add-exp-log
10×unswap-sqr
8×swap-sqr
6×associate-*l/ add-log-exp
5×prod-exp pow-prod-up cbrt-unprod
4×expm1-log1p-u sqrt-unprod sqrt-div insert-posit16 log1p-expm1-u
3×flip3-- prod-diff pow-sqr *-commutative flip--
2×difference-of-squares
1×pow2 sub-neg rem-square-sqrt pow-plus fma-neg diff-log
Counts
4 → 145
Calls
4 calls:
Slowest
111.0ms
(* (* (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
51.0ms
(* (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)) (sqrt (sqrt 2.0)))
14.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
11.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series734.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
353.0ms
(* (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)) (sqrt (sqrt 2.0)))
230.0ms
(* (* (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
90.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
62.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify4.8s

Counts
139 → 157
Calls
139 calls:
Slowest
485.0ms
(* (* (* (* (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)) (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re))) (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
451.0ms
(* (sqrt (- (pow (* (sqrt (hypot re im)) (sqrt (hypot re im))) 3) (pow re 3))) (sqrt (sqrt 2.0)))
404.0ms
(* (* (* (* (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)) (sqrt (sqrt 2.0))) (* (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)) (sqrt (sqrt 2.0)))) (* (sqrt (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)) (sqrt (sqrt 2.0)))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
323.0ms
(* (* (sqrt (- (pow (* (sqrt (hypot re im)) (sqrt (hypot re im))) 3) (pow re 3))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
318.0ms
(* (sqrt (- (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (* re re))) (sqrt (sqrt 2.0)))

prune2.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 14.6b

regimes237.0ms

Accuracy

0% (0.5b remaining)

Error of 13.8b against oracle of 13.3b and baseline of 13.8b

bsearch3.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
806.0ms5991×body80valid
614.0ms279×body640valid
520.0ms689×body2560valid
359.0ms537×body1280valid
262.0ms290×body5120valid
54.0ms85×body160valid
44.0ms129×body320valid