Details

Time bar (total: 7.7s)

sample129.0ms

Algorithm
intervals
Results
47.0ms16×body2560valid
18.0ms208×body80valid
6.0ms11×body1280valid
5.0ms9×body5120valid
2.0ms5×body640valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify62.0ms

Calls
1 calls:
Slowest
62.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.0b

localize15.0ms

Local error

Found 1 expressions with local error:

0.5b
(- (hypot re im) re)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
3×fma-neg
2×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
Calls
1 calls:
Slowest
5.0ms
(- (hypot re im) re)

series62.0ms

Calls
1 calls:
Slowest
62.0ms
(- (hypot re im) re)

simplify42.0ms

Calls
5 calls:
Slowest
18.0ms
(* -2 re)
8.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
6.0ms
(sqrt (hypot re im))
6.0ms
(- im re)
2.0ms
0

prune192.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 9.9b

localize14.0ms

Local error

Found 1 expressions with local error:

11.8b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Calls
1 calls:
Slowest
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series84.0ms

Calls
1 calls:
Slowest
83.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify5.0ms

Calls
3 calls:
Slowest
3.0ms
(- im re)
0.0ms
(- (+ re (- (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))))
0.0ms
(- (+ re (- (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))))

prune164.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.8b

localize24.0ms

Local error

Found 2 expressions with local error:

5.6b
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt *-un-lft-identity associate-*r* associate-*l* add-cube-cbrt sqrt-prod
4×add-cbrt-cube pow1/2 add-exp-log add-log-exp
2×expm1-log1p-u pow-prod-down pow-prod-up insert-posit16 log1p-expm1-u
1×pow2 neg-sub0 +-commutative associate-+r- sum-log rem-square-sqrt fma-def flip3-+ pow-plus sqrt-unprod unsub-neg prod-exp *-commutative cbrt-unprod flip-+
Calls
2 calls:
Slowest
15.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
12.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

series87.0ms

Calls
2 calls:
Slowest
48.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
39.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify272.0ms

Calls
29 calls:
Slowest
71.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
69.0ms
(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp (- re)))
9.0ms
(sqrt (hypot re im))
9.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.0ms
(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))

prune550.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.8b

localize36.0ms

Local error

Found 4 expressions with local error:

7.8b
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) (- re))
0.3b
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
0.3b
(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
0.1b
(sqrt (sqrt (hypot re im)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
33×sqrt-prod
20×add-sqr-sqrt
18×associate-*l*
15×pow1
14×*-un-lft-identity add-cube-cbrt
12×pow1/2
11×add-cbrt-cube add-exp-log
7×associate-*r* pow-prod-down
6×pow-prod-up add-log-exp
4×expm1-log1p-u cube-unmult prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×sqrt-unprod
2×rem-sqrt-square pow-plus *-commutative
1×neg-sub0 +-commutative associate-+r- sum-log fma-def flip3-+ unsub-neg flip-+
Calls
4 calls:
Slowest
32.0ms
(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
15.0ms
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) (- re))
6.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
3.0ms
(sqrt (sqrt (hypot re im)))

series282.0ms

Calls
4 calls:
Slowest
123.0ms
(sqrt (sqrt (hypot re im)))
99.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
36.0ms
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) (- re))
23.0ms
(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))

simplify1.2s

Calls
69 calls:
Slowest
233.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im)))))
208.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))))
104.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
89.0ms
(* (exp (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (exp (- re)))
86.0ms
(+ (pow im 3/4) (* 3/8 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/4))))

prune1.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 9.8b

regimes262.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch2.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
925.0ms649×body2560valid
845.0ms6027×body80valid
336.0ms511×body1280valid
285.0ms307×body5120valid
153.0ms277×body640valid
51.0ms155×body320valid
16.0ms74×body160valid