Details

Time bar (total: 23.2s)

sample319.0ms

Algorithm
intervals
Results
56.0ms17×body2560valid
33.0ms190×body80valid
14.0ms17×body1280valid
11.0ms10×body5120valid
9.0ms13×body640valid
3.0ms6×body320valid
1.0ms3×body160valid

simplify112.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
111.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize32.0ms

Local error

Found 2 expressions with local error:

0.7b
(- (hypot re im) re)
0.0b
(sqrt (* (- (hypot re im) re) 2.0))

rewrite42.0ms

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
16.0ms
(sqrt (* (- (hypot re im) re) 2.0))
13.0ms
(- (hypot re im) re)

series435.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
313.0ms
(sqrt (* (- (hypot re im) re) 2.0))
122.0ms
(- (hypot re im) re)

simplify2.4s

Counts
65 → 51
Calls
65 calls:
Slowest
442.0ms
(* (* (- (hypot re im) re) (- (hypot re im) re)) (- (hypot re im) re))
195.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
185.0ms
(* (* (sqrt (* (- (hypot re im) re) 2.0)) (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (* (- (hypot re im) re) 2.0)))
162.0ms
(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
110.0ms
(- (pow (hypot re im) 3) (pow re 3))

prune488.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.1b

localize28.0ms

Local error

Found 4 expressions with local error:

16.1b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0b
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt
7×sqrt-prod
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/2
2×rem-sqrt-square
1×pow-prod-down fma-udef
Counts
4 → 57
Calls
4 calls:
Slowest
8.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
2.0ms
(sqrt (hypot re im))
2.0ms
(sqrt (hypot re im))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
617.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
329.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
114.0ms
(sqrt (hypot re im))
110.0ms
(sqrt (hypot re im))

simplify1.9s

Counts
71 → 69
Calls
71 calls:
Slowest
518.0ms
(* (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
228.0ms
(* (* (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)) (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))) (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
91.0ms
(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
84.0ms
(exp (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
74.0ms
(log (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))

prune669.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.0b

localize30.0ms

Local error

Found 4 expressions with local error:

16.1b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
16.1b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.4b
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
0.0b
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×sqrt-prod
20×pow1
13×*-un-lft-identity add-cube-cbrt
9×sqrt-pow1 pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×fma-udef
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 90
Calls
4 calls:
Slowest
9.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
1.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series893.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
245.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
239.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
232.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
178.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))

simplify4.0s

Counts
112 → 102
Calls
112 calls:
Slowest
461.0ms
(* (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
450.0ms
(* (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
371.0ms
(* (* (* (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 (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)))))
245.0ms
(* (* (* (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 (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)))))
174.0ms
(exp (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))))

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.0b

localize50.0ms

Local error

Found 4 expressions with local error:

16.1b
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))
0.5b
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.1b
(sqrt (sqrt (hypot re im)))
0.1b
(sqrt (sqrt (hypot re im)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
86×sqrt-prod
54×add-sqr-sqrt
40×sqrt-pow1
31×pow1
20×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×expm1-log1p-u rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 133
Calls
4 calls:
Slowest
13.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
2.0ms
(sqrt (sqrt (hypot re im)))
2.0ms
(sqrt (sqrt (hypot re im)))
0.0ms
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

series675.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))
181.0ms
(sqrt (sqrt (hypot re im)))
154.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
154.0ms
(sqrt (sqrt (hypot re im)))

simplify3.6s

Counts
172 → 145
Calls
172 calls:
Slowest
219.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
214.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
210.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))
180.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))
141.0ms
(exp (fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re)))

prune1.8s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 14.0b

regimes198.0ms

Accuracy

0% (0.3b remaining)

Error of 13.6b against oracle of 13.4b and baseline of 13.6b

bsearch3.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
849.0ms6007×body80valid
718.0ms272×body5120valid
593.0ms709×body2560valid
349.0ms498×body1280valid
182.0ms311×body640valid
48.0ms145×body320valid
12.0ms58×body160valid