Details

Time bar (total: 23.1s)

sample130.0ms

Algorithm
intervals
Results
55.0ms198×body80valid
9.0ms20×body2560valid
7.0ms19×body1280valid
4.0ms8×body5120valid
1.0ms6×body320valid
1.0ms4×body640valid
0.0ms1×body160valid

simplify78.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
77.0ms
(* 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: 12.9b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

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
8.0ms
(sqrt (* (- (hypot re im) re) 2.0))
7.0ms
(- (hypot re im) re)
0.0ms
(hypot re im)

series402.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
264.0ms
(sqrt (* (- (hypot re im) re) 2.0))
82.0ms
(- (hypot re im) re)
55.0ms
(hypot re im)

simplify935.0ms

Counts
38 → 65
Calls
38 calls:
Slowest
255.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
135.0ms
(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
55.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* re 1)))
49.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
48.0ms
(* (- (hypot re im) re) 2.0)

prune636.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (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)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
22×*-un-lft-identity
17×sqrt-prod
16×add-cube-cbrt
9×pow1 prod-diff
8×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×sqrt-pow1 flip3-- pow1/2 fma-neg pow-prod-down flip-- distribute-lft-out-- difference-of-squares
2×associate-*l/
1×rem-sqrt-square hypot-udef sub-neg sqrt-unprod diff-log prod-exp *-commutative cbrt-unprod
Counts
4 → 97
Calls
4 calls:
Slowest
25.0ms
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
11.0ms
(- (hypot re im) re)
6.0ms
(sqrt (- (hypot re im) re))
0.0ms
(hypot re im)

series637.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
315.0ms
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
174.0ms
(sqrt (- (hypot re im) re))
75.0ms
(- (hypot re im) re)
72.0ms
(hypot re im)

simplify2.3s

Counts
75 → 109
Calls
75 calls:
Slowest
372.0ms
(* (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) (sqrt (- (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
237.0ms
(sqrt (- (pow (hypot re im) 3) (pow re 3)))
237.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt 2.0))
199.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))
166.0ms
(sqrt (- (* (hypot re im) (hypot re im)) (* re re)))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.5b

localize44.0ms

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

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
37×sqrt-prod
26×*-un-lft-identity
20×add-cube-cbrt
18×associate-*r*
17×pow1
11×add-cbrt-cube add-exp-log
10×pow-prod-down
9×associate-*l* prod-diff
6×sqrt-pow1 pow1/2 sqrt-div associate-*l/ add-log-exp unswap-sqr
4×expm1-log1p-u flip3-- prod-exp cbrt-unprod insert-posit16 log1p-expm1-u flip--
3×fma-neg sqrt-unprod distribute-lft-out-- difference-of-squares
2×*-commutative
1×rem-sqrt-square sub-neg diff-log
Counts
4 → 123
Calls
4 calls:
Slowest
69.0ms
(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
22.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
16.0ms
(- (hypot re im) re)
13.0ms
(sqrt (- (hypot re im) re))

series937.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
355.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
296.0ms
(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
201.0ms
(sqrt (- (hypot re im) re))
85.0ms
(- (hypot re im) re)

simplify3.8s

Counts
104 → 135
Calls
104 calls:
Slowest
410.0ms
(* (* (* (* (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))))
314.0ms
(* (* (* (* (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))))
279.0ms
(* (* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
231.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (sqrt 2.0)))
207.0ms
(sqrt (- (pow (hypot re im) 3) (pow re 3)))

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (- (hypot re im) re) (sqrt 2.0))
0.3b
(- (hypot re im) re)
0.3b
(* (sqrt (* (- (hypot re im) re) (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.1b
(sqrt (* (- (hypot re im) re) (sqrt 2.0)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
22×*-un-lft-identity
18×add-cube-cbrt sqrt-prod
16×pow1
15×associate-*r*
9×associate-*l* prod-diff
8×add-cbrt-cube associate-*l/ add-exp-log
7×pow-prod-down
6×sqrt-pow1 add-log-exp
5×unswap-sqr
4×expm1-log1p-u flip3-- sqrt-div insert-posit16 log1p-expm1-u flip--
3×pow1/2 fma-neg
2×prod-exp *-commutative cbrt-unprod distribute-lft-out-- difference-of-squares
1×sub-neg sqrt-unprod diff-log
Counts
4 → 110
Calls
4 calls:
Slowest
73.0ms
(* (sqrt (* (- (hypot re im) re) (sqrt 2.0))) (sqrt (sqrt 2.0)))
18.0ms
(* (- (hypot re im) re) (sqrt 2.0))
12.0ms
(sqrt (* (- (hypot re im) re) (sqrt 2.0)))
5.0ms
(- (hypot re im) re)

series945.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
396.0ms
(sqrt (* (- (hypot re im) re) (sqrt 2.0)))
278.0ms
(* (sqrt (* (- (hypot re im) re) (sqrt 2.0))) (sqrt (sqrt 2.0)))
175.0ms
(* (- (hypot re im) re) (sqrt 2.0))
96.0ms
(- (hypot re im) re)

simplify4.3s

Counts
88 → 122
Calls
88 calls:
Slowest
433.0ms
(* (* (* (sqrt (* (- (hypot re im) re) (sqrt 2.0))) (sqrt (* (- (hypot re im) re) (sqrt 2.0)))) (sqrt (* (- (hypot re im) re) (sqrt 2.0)))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
322.0ms
(* (sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) (sqrt 2.0))) (sqrt (sqrt 2.0)))
311.0ms
(* (* (* (- (hypot re im) re) (- (hypot re im) re)) (- (hypot re im) re)) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
310.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) (sqrt 2.0)))
291.0ms
(* (- (* (hypot re im) (hypot re im)) (* re re)) (sqrt 2.0))

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.5b

regimes161.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch2.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
827.0ms6049×body80valid
819.0ms483×body1280valid
646.0ms678×body2560valid
333.0ms284×body5120valid
131.0ms269×body640valid
109.0ms155×body320valid
20.0ms82×body160valid