Details

Time bar (total: 23.8s)

sample91.0ms

Algorithm
intervals
Results
28.0ms194×body80valid
21.0ms24×body2560valid
11.0ms10×body5120valid
8.0ms11×body1280valid
6.0ms10×body640valid
2.0ms5×body320valid
1.0ms2×body160valid

simplify58.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
58.0ms
(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ (hypot re im) re)
0.0b
(sqrt (* (+ (hypot re im) re) 2.0))
0.0b
(hypot re im)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 *-un-lft-identity
5×add-log-exp
4×add-sqr-sqrt add-cube-cbrt
3×expm1-log1p-u fma-def add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×sqrt-pow1 flip3-+ sqrt-div associate-*l/ flip-+
1×+-commutative hypot-udef sum-log pow1/2 pow-prod-down sqrt-prod distribute-lft-out
Counts
3 → 45
Calls
3 calls:
Slowest
12.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms
(+ (hypot re im) re)
0.0ms
(hypot re im)

series432.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
267.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
92.0ms
(+ (hypot re im) re)
72.0ms
(hypot re im)

simplify509.0ms

Counts
18 → 54
Calls
18 calls:
Slowest
238.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
170.0ms
(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
27.0ms
(* (+ (hypot re im) re) 2.0)
16.0ms
(* (+ (hypot re im) re) 2.0)
12.0ms
(* (exp (hypot re im)) (exp re))

prune506.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

localize34.0ms

Local error

Found 4 expressions with local error:

8.3b
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b
(hypot re im)
0.0b
(hypot re im)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×pow1
18×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
8×sqrt-pow1 pow1/2 swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log add-log-exp
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u unswap-sqr
3×pow-prod-down pow-sqr
2×hypot-udef
1×pow2 +-commutative sum-log rem-square-sqrt fma-def flip3-+ pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 89
Calls
4 calls:
Slowest
9.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
9.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0ms
(hypot re im)
0.0ms
(hypot re im)

series319.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
83.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
65.0ms
(hypot re im)
63.0ms
(hypot re im)

simplify820.0ms

Counts
73 → 101
Calls
73 calls:
Slowest
146.0ms
(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp re))
139.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
113.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
18.0ms
(+ (/ 1 2) 1/2)
15.0ms
(* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))))

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.2b

localize50.0ms

Local error

Found 4 expressions with local error:

8.3b
(+ (* (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)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
55×sqrt-pow1
52×pow1
42×sqrt-prod
36×pow-prod-up
33×pow1/2
32×add-sqr-sqrt
18×associate-*l*
14×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×pow-prod-down
7×associate-*r*
6×pow-plus add-log-exp unswap-sqr
4×expm1-log1p-u cube-unmult prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×sqrt-unprod
2×rem-sqrt-square *-commutative
1×+-commutative sum-log fma-def flip3-+ flip-+
Counts
4 → 133
Calls
4 calls:
Slowest
47.0ms
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)
35.0ms
(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
11.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
2.0ms
(sqrt (sqrt (hypot re im)))

series523.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
202.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
172.0ms
(sqrt (sqrt (hypot re im)))
85.0ms
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)
64.0ms
(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))

simplify3.1s

Counts
127 → 145
Calls
127 calls:
Slowest
457.0ms
(* (* (* (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))))
397.0ms
(* (* (* (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)))))
386.0ms
(* (* (* (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)))))
315.0ms
(* (exp (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (exp re))
221.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))

prune1.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.2b

localize37.0ms

Local error

Found 4 expressions with local error:

4.6b
(+ (* (sqrt (sqrt (hypot re im))) (pow (hypot re im) 3/4)) re)
0.3b
(* (sqrt (sqrt (hypot re im))) (pow (hypot re im) 3/4))
0.1b
(sqrt (sqrt (hypot re im)))
0.0b
(pow (hypot re im) 3/4)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
28×sqrt-prod
13×*-un-lft-identity add-cube-cbrt
10×add-exp-log
9×unpow-prod-down associate-*l* unswap-sqr
8×pow1
7×sqrt-pow1 associate-*r*
6×add-cbrt-cube add-log-exp
5×sqr-pow
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow-unpow pow1/2 prod-exp
2×pow-to-exp rem-sqrt-square pow-exp pow-prod-up
1×+-commutative hypot-udef sum-log pow-pow fma-def flip3-+ *-commutative cbrt-unprod flip-+ sqrt-pow2
Counts
4 → 100
Calls
4 calls:
Slowest
30.0ms
(* (sqrt (sqrt (hypot re im))) (pow (hypot re im) 3/4))
16.0ms
(+ (* (sqrt (sqrt (hypot re im))) (pow (hypot re im) 3/4)) re)
2.0ms
(pow (hypot re im) 3/4)
2.0ms
(sqrt (sqrt (hypot re im)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(pow (hypot re im) 3/4)
146.0ms
(sqrt (sqrt (hypot re im)))
73.0ms
(* (sqrt (sqrt (hypot re im))) (pow (hypot re im) 3/4))
71.0ms
(+ (* (sqrt (sqrt (hypot re im))) (pow (hypot re im) 3/4)) re)

simplify9.2s

Counts
74 → 112
Calls
74 calls:
Slowest
941.0ms
(* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (hypot re im)) 3/4))
552.0ms
(* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (hypot re im)) 3/4))
505.0ms
(* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (hypot re im)) 3/4))
503.0ms
(* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (hypot re im)) 3/4))
472.0ms
(* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (hypot re im)) 3/4))

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.2b

regimes205.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch3.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.0s732×body2560valid
894.0ms6011×body80valid
325.0ms481×body1280valid
279.0ms293×body5120valid
115.0ms259×body640valid
51.0ms155×body320valid
15.0ms69×body160valid