Details

Time bar (total: 18.9s)

sample206.0ms

Algorithm
intervals
Results
32.0ms207×body80valid
21.0ms24×body2560valid
7.0ms11×body1280valid
4.0ms4×body5120valid
3.0ms6×body640valid
1.0ms3×body320valid
0.0ms1×body160valid

simplify111.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
110.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.2b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

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
15.0ms
(sqrt (* (- (hypot re im) re) 2.0))
12.0ms
(- (hypot re im) re)
0.0ms
(hypot re im)

series458.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
260.0ms
(sqrt (* (- (hypot re im) re) 2.0))
120.0ms
(- (hypot re im) re)
78.0ms
(hypot re im)

simplify1.1s

Counts
38 → 65
Calls
38 calls:
Slowest
256.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
192.0ms
(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
76.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
56.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (sqrt re) (sqrt re))))
40.0ms
(* (- (hypot re im) re) 2.0)

prune630.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
0.3b
(- (hypot re im) re)
0.3b
(- (hypot re im) re)
0.0b
(sqrt (- (hypot re im) re))

rewrite78.0ms

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
50.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
11.0ms
(- (hypot re im) re)
9.0ms
(- (hypot re im) re)
6.0ms
(sqrt (- (hypot re im) re))

series436.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(sqrt (- (hypot re im) re))
88.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
86.0ms
(- (hypot re im) re)
82.0ms
(- (hypot re im) re)

simplify4.5s

Counts
153 → 158
Calls
153 calls:
Slowest
278.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (pow (hypot re im) 3) (pow re 3))))
275.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (- (* (hypot re im) (hypot re im)) (* re re))))
273.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (hypot re im) re)))
232.0ms
(sqrt (- (pow (hypot re im) 3) (pow re 3)))
230.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (- (hypot re im) re)))

prune1.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.0b

localize24.0ms

Local error

Found 4 expressions with local error:

6.3b
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×sqrt-prod
21×pow1
15×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 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 insert-posit16 log1p-expm1-u unswap-sqr
3×prod-diff pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 sub-neg rem-square-sqrt pow-plus flip3-- fma-neg sqrt-unprod diff-log prod-exp *-commutative cbrt-unprod flip-- difference-of-squares
Counts
4 → 104
Calls
4 calls:
Slowest
10.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
8.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
1.0ms
(sqrt (hypot re im))
1.0ms
(sqrt (hypot re im))

series400.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(sqrt (hypot re im))
111.0ms
(sqrt (hypot re im))
89.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
65.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.0s

Counts
91 → 116
Calls
91 calls:
Slowest
189.0ms
(/ (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))))
78.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
31.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
26.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- (* re 1)))

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.0b

localize70.0ms

Local error

Found 4 expressions with local error:

6.1b
(- (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im)))) re)
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×pow1/3 prod-diff
1×sub-neg flip3-- fma-neg diff-log flip--
Counts
4 → 61
Calls
4 calls:
Slowest
138.0ms
(- (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im)))) re)
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))

series628.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(cbrt (hypot re im))
178.0ms
(cbrt (hypot re im))
165.0ms
(cbrt (hypot re im))
78.0ms
(- (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im)))) re)

simplify1.5s

Counts
29 → 73
Calls
29 calls:
Slowest
412.0ms
(/ (exp (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im))))) (exp re))
225.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
217.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
185.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
70.0ms
(fma (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im))) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.0b

regimes244.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch2.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
846.0ms6018×body80valid
669.0ms289×body640valid
566.0ms687×body2560valid
351.0ms498×body1280valid
286.0ms276×body5120valid
54.0ms155×body320valid
20.0ms77×body160valid