Details

Time bar (total: 16.7s)

sample93.0ms

Algorithm
intervals
Results
25.0ms181×body80valid
21.0ms23×body2560valid
15.0ms21×body1280valid
8.0ms8×body5120valid
8.0ms14×body640valid
2.0ms5×body320valid
1.0ms4×body160valid

simplify78.0ms

Calls
1 calls:
Slowest
78.0ms
(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.8b

localize26.0ms

Local error

Found 2 expressions with local error:

1.0b
(+ (hypot re im) re)
0.0b
(sqrt (* (+ (hypot re im) re) 2.0))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
13×sqrt-prod
11×add-sqr-sqrt
10×*-un-lft-identity
6×add-cube-cbrt
5×pow1
4×associate-*l* add-log-exp
3×fma-def associate-*r*
2×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube sqrt-div associate-*l/ add-exp-log flip-+ insert-posit16 log1p-expm1-u distribute-lft-out unswap-sqr
1×+-commutative sum-log pow1/2 pow-prod-down *-commutative
Calls
2 calls:
Slowest
42.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms
(+ (hypot re im) re)

series342.0ms

Calls
2 calls:
Slowest
246.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
95.0ms
(+ (hypot re im) re)

simplify722.0ms

Calls
29 calls:
Slowest
220.0ms
(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
197.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
38.0ms
(sqrt (* (+ (hypot re im) re) (* (cbrt 2.0) (cbrt 2.0))))
32.0ms
(sqrt (* (cbrt (* (+ (hypot re im) re) 2.0)) (cbrt (* (+ (hypot re im) re) 2.0))))
32.0ms
(sqrt (* (+ (hypot re im) re) 1))

prune605.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 16.5b

localize26.0ms

Local error

Found 4 expressions with local error:

18.2b
(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))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))

rewrite17.0ms

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
12.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
2.0ms
(sqrt (hypot re im))
2.0ms
(sqrt (hypot re im))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series839.0ms

Calls
4 calls:
Slowest
359.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
207.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
147.0ms
(sqrt (hypot re im))
125.0ms
(sqrt (hypot re im))

simplify555.0ms

Calls
38 calls:
Slowest
123.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) (* (cbrt 2.0) (cbrt 2.0))))
57.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
55.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) (sqrt 2.0)))
48.0ms
(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
43.0ms
(sqrt (* (cbrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)) (cbrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))

prune951.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 16.3b

localize15.0ms

Local error

Found 4 expressions with local error:

12.2b
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.0b
(sqrt (hypot re im))

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
53×sqrt-prod
33×*-un-lft-identity
29×fma-def
25×add-cube-cbrt
23×pow1
19×associate-*l*
16×swap-sqr
15×associate-*r*
11×sqrt-pow1
10×pow1/2 unswap-sqr
6×add-cbrt-cube add-exp-log add-log-exp
5×pow-prod-up
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u distribute-lft-out
3×rem-sqrt-square pow-sqr *-commutative
2×flip3-+ sqrt-div associate-*l/ flip-+
1×pow2 +-commutative sum-log rem-square-sqrt pow-plus sqrt-unprod prod-exp cbrt-unprod
Calls
4 calls:
Slowest
186.0ms
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
52.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
9.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
1.0ms
(sqrt (hypot re im))

series526.0ms

Calls
4 calls:
Slowest
269.0ms
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
120.0ms
(sqrt (hypot re im))
70.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
68.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify2.5s

Calls
126 calls:
Slowest
389.0ms
(sqrt (* (- (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (* re re)) 2.0))
332.0ms
(sqrt (* (+ (pow (* (sqrt (hypot re im)) (sqrt (hypot re im))) 3) (pow re 3)) 2.0))
186.0ms
(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp re))
136.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
101.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))

prune1.7s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 16.3b

localize39.0ms

Local error

Found 4 expressions with local error:

18.2b
(fma (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))) re)
0.4b
(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
0.1b
(sqrt (sqrt (hypot re im)))
0.1b
(sqrt (sqrt (hypot re im)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
31×add-sqr-sqrt
19×pow1 sqrt-pow1
13×*-un-lft-identity add-cube-cbrt
11×pow1/2
9×associate-*r*
6×add-cbrt-cube associate-*l* add-exp-log pow-prod-up unswap-sqr
4×expm1-log1p-u rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down
2×pow3
1×sqrt-unprod prod-exp *-commutative cbrt-unprod fma-udef
Calls
4 calls:
Slowest
22.0ms
(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
3.0ms
(sqrt (sqrt (hypot re im)))
3.0ms
(sqrt (sqrt (hypot re im)))
1.0ms
(fma (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))) re)

series696.0ms

Calls
4 calls:
Slowest
204.0ms
(fma (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))) re)
178.0ms
(sqrt (sqrt (hypot re im)))
161.0ms
(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
153.0ms
(sqrt (sqrt (hypot re im)))

simplify1.8s

Calls
81 calls:
Slowest
505.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))
220.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
212.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
203.0ms
(+ (pow im 3/4) (* 3/8 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/4))))
29.0ms
(pow (/ 1 re) -3/4)

prune1.4s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 16.3b

regimes341.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch2.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
893.0ms6061×body80valid
768.0ms425×body1280valid
643.0ms717×body2560valid
292.0ms299×body640valid
239.0ms273×body5120valid
55.0ms156×body320valid
18.0ms69×body160valid