Details

Time bar (total: 17.2s)

sample83.0ms

Algorithm
intervals
Results
25.0ms192×body80valid
21.0ms25×body2560valid
10.0ms15×body1280valid
8.0ms13×body640valid
5.0ms5×body5120valid
3.0ms6×body320valid

simplify44.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
44.0ms
(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.8b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

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))
10.0ms
(+ (hypot re im) re)
0.0ms
(hypot re im)

series447.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
272.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
103.0ms
(+ (hypot re im) re)
72.0ms
(hypot re im)

simplify575.0ms

Counts
18 → 54
Calls
18 calls:
Slowest
263.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
189.0ms
(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
29.0ms
(* (+ (hypot re im) re) 2.0)
25.0ms
(* (+ (hypot re im) re) 2.0)
16.0ms
(* (exp (hypot re im)) (exp re))

prune653.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.4b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×*-un-lft-identity
15×sqrt-prod
10×add-cube-cbrt
9×pow1
7×associate-*l*
6×add-cbrt-cube associate-*r* add-exp-log add-log-exp
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u unswap-sqr
3×fma-def sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ distribute-lft-out
2×associate-*l/
1×+-commutative rem-sqrt-square hypot-udef sum-log sqrt-unprod prod-exp *-commutative cbrt-unprod hypot-def
Counts
4 → 85
Calls
4 calls:
Slowest
33.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
10.0ms
(sqrt (+ (hypot re im) re))
8.0ms
(+ (hypot re im) re)
0.0ms
(hypot re im)

series574.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
269.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
170.0ms
(sqrt (+ (hypot re im) re))
80.0ms
(+ (hypot re im) re)
54.0ms
(hypot re im)

simplify1.6s

Counts
54 → 97
Calls
54 calls:
Slowest
487.0ms
(* (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) (sqrt (+ (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
348.0ms
(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt 2.0))
128.0ms
(sqrt (+ (pow (hypot re im) 3) (pow re 3)))
128.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))
111.0ms
(sqrt (- (* (hypot re im) (hypot re im)) (* re re)))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (hypot re im) re)
0.3b
(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.2b
(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
0.0b
(sqrt (+ (hypot re im) re))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
35×sqrt-prod
29×add-sqr-sqrt
20×*-un-lft-identity
18×associate-*r*
17×pow1
14×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×pow-prod-down
8×associate-*l*
6×sqrt-pow1 pow1/2 sqrt-div associate-*l/ add-log-exp unswap-sqr
4×expm1-log1p-u flip3-+ prod-exp cbrt-unprod flip-+ insert-posit16 log1p-expm1-u
3×fma-def sqrt-unprod distribute-lft-out
2×*-commutative
1×+-commutative rem-sqrt-square sum-log hypot-def
Counts
4 → 111
Calls
4 calls:
Slowest
59.0ms
(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
26.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
9.0ms
(+ (hypot re im) re)
5.0ms
(sqrt (+ (hypot re im) re))

series835.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
326.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
272.0ms
(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
165.0ms
(sqrt (+ (hypot re im) re))
73.0ms
(+ (hypot re im) re)

simplify3.1s

Counts
83 → 123
Calls
83 calls:
Slowest
501.0ms
(* (* (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) (sqrt (+ (hypot re im) re))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
349.0ms
(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt (sqrt 2.0)))
326.0ms
(* (* (* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))) (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
307.0ms
(* (* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
201.0ms
(* (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) (sqrt (+ (hypot re im) re))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.4b

localize38.0ms

Local error

Found 4 expressions with local error:

9.3b
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.3b
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.0b
(hypot re im)

rewrite33.0ms

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
12.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
11.0ms
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
8.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0ms
(hypot re im)

series497.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
285.0ms
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
80.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
68.0ms
(hypot re im)
64.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.6s

Counts
78 → 106
Calls
78 calls:
Slowest
366.0ms
(sqrt (* (- (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (* re re)) 2.0))
358.0ms
(sqrt (* (+ (pow (* (sqrt (hypot re im)) (sqrt (hypot re im))) 3) (pow re 3)) 2.0))
198.0ms
(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp re))
133.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
94.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.3b

regimes211.0ms

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
1.0s699×body2560valid
768.0ms6025×body80valid
368.0ms285×body5120valid
315.0ms496×body1280valid
125.0ms276×body640valid
116.0ms147×body320valid
19.0ms72×body160valid