Details

Time bar (total: 20.5s)

sample136.0ms

Algorithm
intervals
Results
57.0ms187×body80valid
13.0ms22×body2560valid
8.0ms18×body1280valid
7.0ms10×body5120valid
6.0ms10×body640valid
1.0ms5×body160valid
1.0ms4×body320valid

simplify141.0ms

Calls
1 calls:
Slowest
141.0ms
(* 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: 15.2b

localize30.0ms

Local error

Found 2 expressions with local error:

1.4b
(- (hypot re im) re)
0.0b
(sqrt (* (- (hypot re im) re) 2.0))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×*-un-lft-identity
14×sqrt-prod
12×add-cube-cbrt
9×prod-diff
5×pow1 associate-*l*
4×add-log-exp
3×fma-neg associate-*r*
2×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube sqrt-div associate-*l/ add-exp-log insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares unswap-sqr
1×sub-neg pow1/2 diff-log pow-prod-down *-commutative
Calls
2 calls:
Slowest
55.0ms
(sqrt (* (- (hypot re im) re) 2.0))
13.0ms
(- (hypot re im) re)

series394.0ms

Calls
2 calls:
Slowest
298.0ms
(sqrt (* (- (hypot re im) re) 2.0))
96.0ms
(- (hypot re im) re)

simplify1.2s

Calls
50 calls:
Slowest
184.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
153.0ms
(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
118.0ms
(sqrt (* (- (hypot re im) re) (* (cbrt 2.0) (cbrt 2.0))))
63.0ms
(sqrt (* (- (hypot re im) re) (sqrt 2.0)))
58.0ms
(sqrt (sqrt (* (- (hypot re im) re) 2.0)))

prune589.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.9b

localize31.0ms

Local error

Found 4 expressions with local error:

16.7b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0b
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
16×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/2 associate-*r* associate-*l*
2×unswap-sqr
1×pow-prod-down *-commutative fma-udef
Calls
4 calls:
Slowest
6.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
1.0ms
(sqrt (hypot re im))
1.0ms
(sqrt (hypot re im))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series726.0ms

Calls
4 calls:
Slowest
295.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
199.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
134.0ms
(sqrt (hypot re im))
99.0ms
(sqrt (hypot re im))

simplify719.0ms

Calls
38 calls:
Slowest
130.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (* (cbrt 2.0) (cbrt 2.0))))
83.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
65.0ms
(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
59.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
51.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (sqrt 2.0)))

prune872.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 14.8b

localize24.0ms

Local error

Found 4 expressions with local error:

9.9b
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
42×sqrt-prod
31×*-un-lft-identity
29×fma-def
23×add-cube-cbrt
21×pow1
16×swap-sqr
14×associate-*l*
12×associate-*r*
10×sqrt-pow1 pow1/2
8×add-log-exp unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out
3×pow-prod-down pow-sqr
2×rem-sqrt-square sum-log distribute-rgt-neg-in *-commutative
1×pow2 neg-sub0 +-commutative associate-+r- rem-square-sqrt flip3-+ pow-plus sqrt-unprod unsub-neg neg-log prod-exp cbrt-unprod flip-+
Calls
4 calls:
Slowest
52.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
16.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
2.0ms
(sqrt (hypot re im))
2.0ms
(sqrt (hypot re im))

series383.0ms

Calls
4 calls:
Slowest
124.0ms
(sqrt (hypot re im))
116.0ms
(sqrt (hypot re im))
86.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
57.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.6s

Calls
114 calls:
Slowest
269.0ms
(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp (- re)))
207.0ms
(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (/ 1 (exp re)))
151.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
104.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
72.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))

prune1.6s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 14.8b

localize56.0ms

Local error

Found 4 expressions with local error:

8.0b
(+ (* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (- re))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.5b
(* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
77×add-sqr-sqrt
58×associate-*r*
39×fma-def
38×sqrt-prod
34×unswap-sqr
29×*-un-lft-identity
21×add-cube-cbrt
20×associate-*l*
18×cbrt-prod
9×pow1 add-cbrt-cube add-exp-log
8×add-log-exp
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u distribute-lft-out
3×pow-prod-down prod-exp cbrt-unprod
2×sum-log distribute-rgt-neg-in pow1/3
1×neg-sub0 +-commutative associate-+r- flip3-+ unsub-neg neg-log flip-+
Calls
4 calls:
Slowest
99.0ms
(+ (* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (- re))
46.0ms
(* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))

series699.0ms

Calls
4 calls:
Slowest
203.0ms
(* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))
180.0ms
(cbrt (hypot re im))
177.0ms
(cbrt (hypot re im))
139.0ms
(+ (* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (- re))

simplify5.7s

Calls
108 calls:
Slowest
693.0ms
(* (pow (pow re 2) 1/3) (fabs (pow (hypot re im) 1/3)))
611.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))))
454.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (* (fabs (cbrt (hypot re im))) (fabs (cbrt (hypot re im)))) (fabs (cbrt (hypot re im)))) (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im))))))
369.0ms
(- (+ (* 1/3 (* (* (pow re 2) (fabs (pow (hypot re im) 1/3))) (pow (/ 1 (pow im 4)) 1/3))) (* (fabs (pow (hypot re im) 1/3)) (pow (pow im 2) 1/3))) re)
298.0ms
(+ (* 1/3 (* (* (pow re 2) (fabs (pow (hypot re im) 1/3))) (pow (/ 1 (pow im 4)) 1/3))) (* (fabs (pow (hypot re im) 1/3)) (pow (pow im 2) 1/3)))

prune2.2s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 14.8b

regimes393.0ms

Accuracy

0% (0.3b remaining)

Error of 12.7b against oracle of 12.4b and baseline of 12.7b

bsearch3.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
897.0ms661×body2560valid
781.0ms6100×body80valid
305.0ms507×body1280valid
293.0ms269×body5120valid
101.0ms245×body640valid
46.0ms141×body320valid
41.0ms77×body160valid