Details

Time bar (total: 21.4s)

sample85.0ms

Algorithm
intervals
Results
27.0ms196×body80valid
13.0ms16×body2560valid
13.0ms18×body1280valid
10.0ms10×body5120valid
4.0ms7×body640valid
2.0ms6×body160valid
1.0ms3×body320valid

simplify56.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
55.0ms
(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 3 expressions with local error:

1.3b
(+ (hypot re im) re)
0.1b
(sqrt (* (+ (hypot re im) re) 2.0))
0.0b
(hypot re im)

rewrite18.0ms

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))
5.0ms
(+ (hypot re im) re)
0.0ms
(hypot re im)

series395.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
230.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
85.0ms
(+ (hypot re im) re)
80.0ms
(hypot re im)

simplify592.0ms

Counts
18 → 54
Calls
18 calls:
Slowest
246.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
211.0ms
(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
32.0ms
(* (+ (hypot re im) re) 2.0)
29.0ms
(* (+ (hypot re im) re) 2.0)
22.0ms
(* (exp (hypot re im)) (exp re))

prune596.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.1b

localize40.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (hypot re im) re)
1.3b
(+ (hypot re im) re)
0.4b
(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))
0.1b
(sqrt (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) 2.0))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity sqrt-div
27×sqrt-prod
26×add-sqr-sqrt
25×pow1
14×flip3-+ add-cube-cbrt flip-+
12×associate-*l/
11×sqrt-pow1 swap-sqr
9×pow1/2
8×frac-times distribute-lft-out add-log-exp
7×associate-*r* associate-*l*
6×fma-def add-cbrt-cube pow-prod-down add-exp-log
5×pow-prod-up
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u unswap-sqr
3×pow-sqr
2×+-commutative sum-log
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
Slowest
55.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))
42.0ms
(sqrt (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) 2.0))
9.0ms
(+ (hypot re im) re)
9.0ms
(+ (hypot re im) re)

series596.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
308.0ms
(sqrt (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) 2.0))
103.0ms
(+ (hypot re im) re)
93.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))
92.0ms
(+ (hypot re im) re)

simplify5.3s

Counts
112 → 136
Calls
112 calls:
Slowest
375.0ms
(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt (+ (hypot re im) re)))
337.0ms
(sqrt (* (* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt (+ (hypot re im) re))) 2.0))
331.0ms
(sqrt (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (pow (hypot re im) 3) (pow re 3)))) 2.0))
305.0ms
(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt (+ (pow (hypot re im) 3) (pow re 3))))
283.0ms
(sqrt (* (* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (+ (pow (hypot re im) 3) (pow re 3)))) 2.0))

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.1b

localize48.0ms

Local error

Found 4 expressions with local error:

7.1b
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.1b
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.0b
(hypot re im)

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×pow1
19×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1
9×pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log add-log-exp
5×pow-prod-up
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u unswap-sqr
3×pow-sqr
2×flip3-+ sqrt-div associate-*l/ flip-+
1×pow2 +-commutative hypot-udef sum-log rem-square-sqrt fma-def pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 94
Calls
4 calls:
Slowest
23.0ms
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
18.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
17.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0ms
(hypot re im)

series525.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
271.0ms
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
100.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
85.0ms
(hypot re im)
69.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.7s

Counts
78 → 106
Calls
78 calls:
Slowest
359.0ms
(sqrt (* (- (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (* re re)) 2.0))
316.0ms
(sqrt (* (+ (pow (* (sqrt (hypot re im)) (sqrt (hypot re im))) 3) (pow re 3)) 2.0))
179.0ms
(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp re))
137.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
108.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))

prune1.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.1b

localize55.0ms

Local error

Found 4 expressions with local error:

9.8b
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)
0.4b
(* (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))))
0.2b
(sqrt (sqrt (hypot re im)))

rewrite107.0ms

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
57.0ms
(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
25.0ms
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)
18.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
3.0ms
(sqrt (sqrt (hypot re im)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
190.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
135.0ms
(sqrt (sqrt (hypot re im)))
103.0ms
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)
75.0ms
(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))

simplify2.9s

Counts
127 → 145
Calls
127 calls:
Slowest
456.0ms
(* (* (* (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))))
356.0ms
(* (* (* (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)))))
326.0ms
(* (* (* (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)))))
296.0ms
(* (exp (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (exp re))
249.0ms
(+ (pow im 3/4) (* 3/8 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/4))))

prune1.9s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.1b

regimes221.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch3.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
833.0ms6058×body80valid
733.0ms522×body1280valid
621.0ms657×body2560valid
252.0ms279×body5120valid
197.0ms283×body640valid
42.0ms116×body320valid
19.0ms85×body160valid