Details

Time bar (total: 17.5s)

sample128.0ms

Algorithm
intervals
Results
40.0ms17×body1280valid
17.0ms200×body80valid
8.0ms17×body2560valid
5.0ms10×body640valid
3.0ms5×body5120valid
1.0ms4×body320valid
0.0ms3×body160valid

simplify71.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
71.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize17.0ms

Local error

Found 3 expressions with local error:

0.4b
(- (hypot re im) re)
0.1b
(sqrt (* (- (hypot re im) re) 2.0))
0.0b
(hypot re im)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×prod-diff
6×pow1
5×add-log-exp
3×expm1-log1p-u add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
2×sqrt-pow1 flip3-- sqrt-div associate-*l/ flip--
1×hypot-udef sub-neg pow1/2 diff-log pow-prod-down sqrt-prod distribute-lft-out-- difference-of-squares
Counts
3 → 56
Calls
3 calls:
Slowest
7.0ms
(sqrt (* (- (hypot re im) re) 2.0))
7.0ms
(- (hypot re im) re)
0.0ms
(hypot re im)

series367.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
221.0ms
(sqrt (* (- (hypot re im) re) 2.0))
83.0ms
(- (hypot re im) re)
62.0ms
(hypot re im)

simplify1.1s

Counts
38 → 65
Calls
38 calls:
Slowest
262.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
177.0ms
(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
67.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (sqrt re) (sqrt re))))
66.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
46.0ms
(* (- (hypot re im) re) 2.0)

prune643.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
0.4b
(- (hypot re im) re)
0.4b
(- (hypot re im) re)
0.1b
(sqrt (- (hypot re im) re))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
47×*-un-lft-identity
35×sqrt-prod
27×add-cube-cbrt
20×pow1
18×prod-diff
14×sqrt-div
12×swap-sqr
9×sqrt-pow1 flip3-- pow1/2 flip-- distribute-lft-out--
8×associate-*r* associate-*l* add-log-exp
7×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log
5×pow-prod-up
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u unswap-sqr
3×pow-prod-down pow-sqr
2×sub-neg diff-log associate-*l/ associate-*r/
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 146
Calls
4 calls:
Slowest
33.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
11.0ms
(sqrt (- (hypot re im) re))
9.0ms
(- (hypot re im) re)
9.0ms
(- (hypot re im) re)

series454.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(sqrt (- (hypot re im) re))
97.0ms
(- (hypot re im) re)
75.0ms
(- (hypot re im) re)
75.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))

simplify3.8s

Counts
153 → 158
Calls
153 calls:
Slowest
325.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (pow (hypot re im) 3) (pow re 3))))
279.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (- (* (hypot re im) (hypot re im)) (* re re))))
213.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (hypot re im) re)))
195.0ms
(* (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) (sqrt (- (hypot re im) re))) (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) (sqrt (- (hypot re im) re))))
183.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (- (pow (hypot re im) 3) (pow re 3))))

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.2b

localize22.0ms

Local error

Found 4 expressions with local error:

5.3b
(- (* (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)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×pow1
19×sqrt-prod
13×*-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×prod-diff pow-sqr
2×flip3-- sqrt-div associate-*l/ flip--
1×pow2 hypot-udef sub-neg rem-square-sqrt pow-plus fma-neg sqrt-unprod diff-log prod-exp *-commutative cbrt-unprod difference-of-squares
Counts
4 → 99
Calls
4 calls:
Slowest
22.0ms
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
18.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
16.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.0ms
(hypot re im)

series479.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
253.0ms
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
85.0ms
(hypot re im)
75.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
65.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.7s

Counts
86 → 111
Calls
86 calls:
Slowest
358.0ms
(sqrt (* (- (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (* re re)) 2.0))
222.0ms
(sqrt (* (- (pow (* (sqrt (hypot re im)) (sqrt (hypot re im))) 3) (pow re 3)) 2.0))
194.0ms
(/ (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp re))
152.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
84.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.2b

localize50.0ms

Local error

Found 4 expressions with local error:

13.3b
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
0.5b
(cbrt (hypot re im))
0.5b
(cbrt (hypot re im))
0.5b
(cbrt (hypot re im))

rewrite3.0ms

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×fma-udef
Counts
4 → 53
Calls
4 calls:
Slowest
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
0.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series748.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
230.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
190.0ms
(cbrt (hypot re im))
171.0ms
(cbrt (hypot re im))
156.0ms
(cbrt (hypot re im))

simplify753.0ms

Counts
21 → 65
Calls
21 calls:
Slowest
210.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
175.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
171.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
35.0ms
(pow (/ 1 re) -1/3)
27.0ms
(pow (/ -1 re) -1/3)

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.2b

regimes243.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch2.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.3s6080×body80valid
609.0ms700×body2560valid
365.0ms453×body1280valid
252.0ms259×body5120valid
139.0ms297×body640valid
49.0ms139×body320valid
17.0ms72×body160valid