Details

Time bar (total: 15.3s)

sample176.0ms

Algorithm
intervals
Results
27.0ms205×body80valid
18.0ms21×body2560valid
6.0ms9×body1280valid
6.0ms6×body5120valid
4.0ms9×body640valid
4.0ms4×body320valid
0.0ms2×body160valid

simplify777.0ms

Calls
1 calls:
Slowest
776.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize46.0ms

Local error

Found 2 expressions with local error:

0.6b
(- (hypot re im) re)
0.5b
(sqrt (* (- (hypot re im) re) 2.0))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity fma-neg add-cube-cbrt
2×expm1-log1p-u pow1 flip3-- add-cbrt-cube sqrt-div associate-*l/ add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
1×sub-neg pow1/2 sqrt-prod
Calls
2 calls:
Slowest
10.0ms
(- (hypot re im) re)
7.0ms
(sqrt (* (- (hypot re im) re) 2.0))

series163.0ms

Calls
2 calls:
Slowest
95.0ms
(sqrt (* (- (hypot re im) re) 2.0))
67.0ms
(- (hypot re im) re)

simplify445.0ms

Calls
11 calls:
Slowest
253.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
169.0ms
(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
7.0ms
(sqrt (- (hypot re im) re))
3.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
3.0ms
(sqrt (hypot re im))

prune409.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.6b
(- (hypot re im) re)
0.4b
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
0.2b
(sqrt (- (hypot re im) re))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×associate-*l* sqrt-prod
5×pow1 add-cbrt-cube add-exp-log
4×sqrt-div
3×expm1-log1p-u flip3-- pow1/2 fma-neg associate-*r* insert-posit16 log1p-expm1-u flip-- add-log-exp
2×pow-prod-down associate-*l/
1×rem-sqrt-square sub-neg sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
3 calls:
Slowest
9.0ms
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
4.0ms
(sqrt (- (hypot re im) re))
4.0ms
(- (hypot re im) re)

series249.0ms

Calls
3 calls:
Slowest
135.0ms
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
73.0ms
(sqrt (- (hypot re im) re))
40.0ms
(- (hypot re im) re)

simplify1.0s

Calls
32 calls:
Slowest
337.0ms
(* (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) (sqrt (- (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
194.0ms
(sqrt (- (* (hypot re im) (hypot re im)) (* re re)))
181.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))
49.0ms
(sqrt (- (pow (hypot re im) 3) (pow re 3)))
48.0ms
(* (- (hypot re im) re) 2.0)

prune810.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (hypot re im) re)
0.6b
(- (hypot re im) re)
0.5b
(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
0.4b
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-div
14×flip3-- flip--
12×associate-*l/
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
8×frac-times
7×sqrt-prod
6×add-cbrt-cube fma-neg associate-*r* associate-*l* add-exp-log
5×pow1/2
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
2×sub-neg pow-prod-down pow-prod-up
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
27.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
18.0ms
(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
8.0ms
(- (hypot re im) re)
8.0ms
(- (hypot re im) re)

series271.0ms

Calls
4 calls:
Slowest
131.0ms
(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
48.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
48.0ms
(- (hypot re im) re)
44.0ms
(- (hypot re im) re)

simplify3.0s

Calls
59 calls:
Slowest
261.0ms
(sqrt (* (* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (hypot re im) re))) 2.0))
259.0ms
(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (* (hypot re im) (hypot re im)) (* re re)))) 2.0))
246.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (hypot re im) re)))
227.0ms
(sqrt (* (* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (pow (hypot re im) 3) (pow re 3)))) 2.0))
213.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (pow (hypot re im) 3) (pow re 3))))

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.9b

localize40.0ms

Local error

Found 4 expressions with local error:

12.4b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.6b
(- (hypot re im) re)
0.5b
(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (- (hypot re im) re))) 2.0))
0.4b
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (- (hypot re im) re)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×sqrt-prod
6×pow1 add-cbrt-cube sqrt-div associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- pow1/2 fma-neg flip--
2×pow-prod-down associate-*l/
1×sub-neg sqrt-unprod prod-exp *-commutative cbrt-unprod fma-udef
Calls
4 calls:
Slowest
9.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (- (hypot re im) re)))
6.0ms
(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (- (hypot re im) re))) 2.0))
4.0ms
(- (hypot re im) re)
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series709.0ms

Calls
4 calls:
Slowest
303.0ms
(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (- (hypot re im) re))) 2.0))
272.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (- (hypot re im) re)))
105.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
29.0ms
(- (hypot re im) re)

simplify1.0s

Calls
35 calls:
Slowest
208.0ms
(* (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))) (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) (sqrt (- (hypot re im) re))))
202.0ms
(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (- (* (hypot re im) (hypot re im)) (* re re)))) 2.0))
117.0ms
(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (- (pow (hypot re im) 3) (pow re 3)))) 2.0))
96.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (- (hypot re im) re))
80.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (- (hypot re im) re))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.9b

regimes503.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch3.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.4s6025×body80valid
600.0ms677×body2560valid
418.0ms499×body1280valid
262.0ms299×body5120valid
121.0ms257×body640valid
55.0ms154×body320valid
21.0ms89×body160valid