Details

Time bar (total: 9.2s)

sample67.0ms

Algorithm
intervals
Results
16.0ms19×body1280valid
16.0ms35×body2560valid
13.0ms177×body80valid
7.0ms14×body5120valid
2.0ms7×body640valid
1.0ms3×body320valid
0.0ms1×body160valid

simplify60.0ms

Calls
1 calls:
Slowest
59.0ms
(* 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: 16.1b

localize42.0ms

Local error

Found 2 expressions with local error:

0.3b
(+ (hypot re im) re)
0.0b
(sqrt (* (+ (hypot re im) re) 2.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt fma-def *-un-lft-identity add-cube-cbrt
2×expm1-log1p-u pow1 flip3-+ add-cbrt-cube sqrt-div associate-*l/ add-exp-log flip-+ insert-posit16 log1p-expm1-u add-log-exp
1×+-commutative pow1/2 sqrt-prod
Calls
2 calls:
Slowest
7.0ms
(+ (hypot re im) re)
4.0ms
(sqrt (* (+ (hypot re im) re) 2.0))

series375.0ms

Calls
2 calls:
Slowest
277.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
98.0ms
(+ (hypot re im) re)

simplify284.0ms

Calls
11 calls:
Slowest
211.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
49.0ms
(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
7.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
4.0ms
(sqrt (+ (hypot re im) re))
3.0ms
(* 2 re)

prune314.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.0b

localize30.0ms

Local error

Found 2 expressions with local error:

19.2b
(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))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
2×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×pow1/2 sqrt-prod fma-udef
Calls
2 calls:
Slowest
3.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series503.0ms

Calls
2 calls:
Slowest
296.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
206.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify10.0ms

Calls
7 calls:
Slowest
5.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
3.0ms
(+ re im)
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)))
0.0ms
(- (+ (* +nan.0 (* (sqrt 2.0) (pow re 2))) (- (+ (* +nan.0 (* (sqrt 2.0) im)) (- (* +nan.0 (* (sqrt 2.0) re)))))))

prune299.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.9b

localize24.0ms

Local error

Found 3 expressions with local error:

11.0b
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.4b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt sqrt-prod
6×associate-*r* associate-*l*
5×add-cbrt-cube pow1/2 add-exp-log
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×flip3-+ sqrt-div pow-prod-down associate-*l/ pow-prod-up flip-+
1×pow2 +-commutative rem-square-sqrt fma-def pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
3 calls:
Slowest
12.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
12.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.0ms
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))

series420.0ms

Calls
3 calls:
Slowest
252.0ms
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
106.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
62.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify674.0ms

Calls
34 calls:
Slowest
330.0ms
(sqrt (* (- (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (* re re)) 2.0))
144.0ms
(sqrt (* (+ (pow (* (sqrt (hypot re im)) (sqrt (hypot re im))) 3) (pow re 3)) 2.0))
62.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
10.0ms
(sqrt (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re))
8.0ms
(+ 1/2 1/2)

prune847.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 15.9b

localize24.0ms

Local error

Found 4 expressions with local error:

10.0b
(+ (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im)))) re)
0.5b
(cbrt (hypot re im))
0.5b
(cbrt (hypot re im))
0.5b
(cbrt (hypot re im))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×+-commutative fma-def flip3-+ flip-+
Calls
4 calls:
Slowest
44.0ms
(+ (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im)))) re)
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))

series478.0ms

Calls
4 calls:
Slowest
150.0ms
(cbrt (hypot re im))
136.0ms
(cbrt (hypot re im))
132.0ms
(cbrt (hypot re im))
60.0ms
(+ (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im)))) re)

simplify449.0ms

Calls
22 calls:
Slowest
119.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
113.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
96.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
17.0ms
(pow (/ 1 re) -1/3)
14.0ms
(pow (/ 1 re) -1/3)

prune983.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.8b

regimes229.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
824.0ms6009×body80valid
807.0ms434×body1280valid
708.0ms707×body2560valid
264.0ms305×body5120valid
179.0ms307×body640valid
50.0ms147×body320valid
20.0ms91×body160valid