Details

Time bar (total: 18.2s)

sample86.0ms

Algorithm
intervals
Results
26.0ms193×body80valid
20.0ms25×body2560valid
10.0ms11×body5120valid
9.0ms14×body1280valid
4.0ms7×body640valid
2.0ms5×body320valid
0.0ms1×body160valid

simplify70.0ms

Counts
1 → 1

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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))
9.0ms
(+ (hypot re im) re)
0.0ms
(hypot re im)

series442.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
273.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
91.0ms
(+ (hypot re im) re)
78.0ms
(hypot re im)

simplify1.7s

Counts
54 → 54

prune595.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.7b

localize39.0ms

Local error

Found 4 expressions with local error:

8.0b
(+ (* (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))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×*-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×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 +-commutative sum-log rem-square-sqrt fma-def flip3-+ pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 99
Calls
4 calls:
Slowest
12.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
9.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
1.0ms
(sqrt (hypot re im))
1.0ms
(sqrt (hypot re im))

series448.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(sqrt (hypot re im))
125.0ms
(sqrt (hypot re im))
91.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
72.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify2.2s

Counts
111 → 111

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.7b

localize31.0ms

Local error

Found 4 expressions with local error:

8.8b
(+ (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) re)
0.3b
(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
0.3b
(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
0.1b
(sqrt (sqrt (hypot re im)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
50×sqrt-pow1
47×pow1
43×sqrt-prod
34×add-sqr-sqrt
32×pow-prod-up
28×pow1/2
18×associate-*r*
14×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×pow-prod-down
7×associate-*l*
6×pow3 add-log-exp unswap-sqr
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×sqrt-unprod
2×rem-sqrt-square pow-plus *-commutative
1×+-commutative sum-log fma-def flip3-+ flip-+
Counts
4 → 129
Calls
4 calls:
Slowest
54.0ms
(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
40.0ms
(+ (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) re)
19.0ms
(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
3.0ms
(sqrt (sqrt (hypot re im)))

series516.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
211.0ms
(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
150.0ms
(sqrt (sqrt (hypot re im)))
88.0ms
(+ (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) re)
68.0ms
(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))

simplify1.0s

Counts
141 → 141

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize44.0ms

Local error

Found 4 expressions with local error:

8.5b
(+ (* (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (hypot re im))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) re)
0.5b
(cbrt (hypot re im))
0.5b
(cbrt (hypot re im))
0.4b
(* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (hypot re im)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt sqrt-prod
8×pow1
6×cbrt-prod add-cbrt-cube associate-*r* associate-*l* add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u unswap-sqr
3×pow-prod-down
2×sqrt-pow1 pow1/2 pow1/3
1×+-commutative sum-log fma-def flip3-+ sqrt-unprod prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 76
Calls
4 calls:
Slowest
107.0ms
(+ (* (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (hypot re im))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) re)
10.0ms
(* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (hypot re im)))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))

series654.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(+ (* (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (hypot re im))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) re)
181.0ms
(cbrt (hypot re im))
156.0ms
(cbrt (hypot re im))
129.0ms
(* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (hypot re im)))

simplify2.5s

Counts
88 → 88

prune1.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.6b

regimes276.0ms

Accuracy

0% (1.6b remaining)

Error of 14.7b against oracle of 13.1b and baseline of 14.7b

bsearch4.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.3s6041×body80valid
715.0ms706×body2560valid
285.0ms266×body5120valid
261.0ms476×body1280valid
128.0ms278×body640valid
50.0ms140×body320valid
19.0ms93×body160valid