Details

Time bar (total: 19.3s)

sample206.0ms

Algorithm
intervals
Results
39.0ms200×body80valid
18.0ms18×body2560valid
10.0ms12×body1280valid
7.0ms6×body5120valid
6.0ms9×body640valid
4.0ms9×body320valid
1.0ms2×body160valid

simplify156.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
155.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.2b

localize28.0ms

Local error

Found 2 expressions with local error:

1.0b
(- (hypot re im) re)
0.0b
(sqrt (* (- (hypot re im) re) 2.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
5×pow1
4×add-log-exp
3×fma-neg
2×expm1-log1p-u sqrt-pow1 flip3-- add-cbrt-cube sqrt-div associate-*l/ add-exp-log insert-posit16 log1p-expm1-u flip--
1×sub-neg pow1/2 diff-log pow-prod-down sqrt-prod distribute-lft-out-- difference-of-squares
Counts
2 → 45
Calls
2 calls:
Slowest
7.0ms
(sqrt (* (- (hypot re im) re) 2.0))
6.0ms
(- (hypot re im) re)

series355.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
264.0ms
(sqrt (* (- (hypot re im) re) 2.0))
91.0ms
(- (hypot re im) re)

simplify1.0s

Counts
35 → 51
Calls
35 calls:
Slowest
220.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
173.0ms
(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)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
43.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* re 1)))
36.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))

prune374.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.9b

localize27.0ms

Local error

Found 2 expressions with local error:

1.0b
(- (hypot re im) re)
0.4b
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
17×*-un-lft-identity
13×add-cube-cbrt
12×sqrt-prod
9×prod-diff
8×associate-*l*
6×pow1 associate-*r*
4×add-cbrt-cube add-exp-log add-log-exp unswap-sqr
3×fma-neg pow-prod-down
2×expm1-log1p-u sqrt-pow1 flip3-- pow1/2 sqrt-div associate-*l/ insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares
1×sub-neg sqrt-unprod diff-log prod-exp *-commutative cbrt-unprod
Counts
2 → 66
Calls
2 calls:
Slowest
21.0ms
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
9.0ms
(- (hypot re im) re)

series346.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
280.0ms
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
66.0ms
(- (hypot re im) re)

simplify1.6s

Counts
60 → 72
Calls
60 calls:
Slowest
364.0ms
(* (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) (sqrt (- (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
165.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt 2.0))
157.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))
65.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
44.0ms
(fma 1 (hypot re im) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))

prune727.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 11.9b

localize29.0ms

Local error

Found 3 expressions with local error:

1.0b
(- (hypot re im) re)
0.2b
(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
0.2b
(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
32×sqrt-prod
22×*-un-lft-identity
18×associate-*r* add-cube-cbrt
15×pow1
10×add-cbrt-cube pow-prod-down add-exp-log
9×associate-*l* prod-diff
6×associate-*l/ unswap-sqr
5×sqrt-pow1 pow1/2 add-log-exp
4×sqrt-div prod-exp cbrt-unprod
3×expm1-log1p-u flip3-- fma-neg sqrt-unprod insert-posit16 log1p-expm1-u flip--
2×*-commutative distribute-lft-out-- difference-of-squares
1×sub-neg diff-log
Counts
3 → 103
Calls
3 calls:
Slowest
68.0ms
(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
18.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
5.0ms
(- (hypot re im) re)

series736.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
385.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
258.0ms
(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
93.0ms
(- (hypot re im) re)

simplify3.7s

Counts
92 → 112
Calls
92 calls:
Slowest
515.0ms
(* (* (* (* (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))))
378.0ms
(* (* (* (* (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))))
277.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (sqrt 2.0)))
239.0ms
(* (* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
204.0ms
(* (* (* (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))))

prune1.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 11.9b

localize32.0ms

Local error

Found 3 expressions with local error:

13.5b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.3b
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (sqrt 2.0)))
0.3b
(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-prod
23×add-sqr-sqrt
18×associate-*r*
15×pow1
11×*-un-lft-identity add-cube-cbrt
10×add-cbrt-cube pow-prod-down add-exp-log
7×associate-*l*
6×unswap-sqr
5×sqrt-pow1 pow1/2
4×prod-exp cbrt-unprod
3×expm1-log1p-u sqrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative
1×fma-udef
Counts
3 → 79
Calls
3 calls:
Slowest
46.0ms
(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
10.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (sqrt 2.0)))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series1.1s

Counts
3 → 9
Calls
3 calls:
Slowest
551.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (sqrt 2.0)))
367.0ms
(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
187.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.7s

Counts
62 → 88
Calls
62 calls:
Slowest
498.0ms
(* (* (* (* (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 (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
402.0ms
(* (* (* (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 (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
381.0ms
(* (* (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (sqrt 2.0))) (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (sqrt 2.0)))) (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (sqrt 2.0)))) (* (* (sqrt (sqrt 2.0)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
129.0ms
(* (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (sqrt 2.0)) (sqrt 2.0))
119.0ms
(* (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (sqrt 2.0)) (sqrt 2.0))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.9b

regimes186.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch2.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
986.0ms669×body2560valid
906.0ms6062×body80valid
351.0ms482×body1280valid
279.0ms291×body5120valid
206.0ms274×body640valid
57.0ms153×body320valid
16.0ms69×body160valid