Details

Time bar (total: 1.2m)

sample1.0s

Algorithm
intervals
Results
736.0ms256×body10240exit
198.0ms550×body80nan
57.0ms256×body80valid

simplify27.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
27.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize76.0ms

Local error

Found 4 expressions with local error:

29.8b
(sqrt (+ (* re re) (* im im)))
0.5b
(* (log base) (log base))
0.3b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1
20×add-sqr-sqrt add-cbrt-cube add-exp-log
17×*-un-lft-identity
15×add-cube-cbrt
12×log-prod
10×associate-*l* log-pow
8×associate-*r*
6×distribute-rgt-in distribute-lft-in swap-sqr prod-exp cbrt-unprod
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down *-commutative unswap-sqr
1×pow2 rem-sqrt-square clear-num associate-/r* frac-2neg flip3-+ times-frac pow-plus pow-sqr pow-prod-up flip-+ div-inv associate-/l*
Counts
4 → 104
Calls
4 calls:
Slowest
41.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
24.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
16.0ms
(* (log base) (log base))
14.0ms
(sqrt (+ (* re re) (* im im)))

series562.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(* (log base) (log base))
155.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
138.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
49.0ms
(sqrt (+ (* re re) (* im im)))

simplify6.9s

Counts
83 → 116
Calls
83 calls:
Slowest
774.0ms
(/ (* (* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))))
684.0ms
(/ (* (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log base) (log base)) (log base))) (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))))
662.0ms
(/ (* (* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))))
607.0ms
(- (+ (log (log (sqrt (+ (* re re) (* im im))))) (log (log base))) (+ (log (log base)) (log (log base))))
508.0ms
(/ (* (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log base) (log base)) (log base))) (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))))

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.7b

localize35.0ms

Local error

Found 3 expressions with local error:

29.8b
(sqrt (+ (* re re) (* im im)))
0.4b
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
0.0b
(+ (* re re) (* im im))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
6×sqrt-pow1 pow1/2 associate-/l*
5×add-cbrt-cube add-exp-log add-log-exp
4×associate-/r* sqrt-div
3×flip3-+ sqrt-prod flip-+ insert-posit16
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg div-exp div-inv
Counts
3 → 77
Calls
3 calls:
Slowest
25.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
12.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(+ (* re re) (* im im))

series249.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
153.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
51.0ms
(sqrt (+ (* re re) (* im im)))
46.0ms
(+ (* re re) (* im im))

simplify3.1s

Counts
76 → 86
Calls
76 calls:
Slowest
539.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log base) (log base)) (log base)))
325.0ms
(/ (log (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (log base))
278.0ms
(sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))
261.0ms
(* -1 (/ (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))
258.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.7b

localize53.0ms

Local error

Found 4 expressions with local error:

29.8b
(sqrt (+ (* re re) (* im im)))
0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
0.3b
(/ 1 (log base))
0.0b
(+ (* re re) (* im im))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
26×times-frac
24×*-un-lft-identity
23×add-cube-cbrt
17×pow1 add-exp-log
16×associate-*r*
11×add-cbrt-cube
10×log-pow
6×associate-*l* add-log-exp
4×associate-/r* div-exp prod-exp insert-posit16
3×sqrt-prod associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-pow1 flip3-+ pow1/2 sqrt-div 1-exp cbrt-unprod flip-+ div-inv
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 107
Calls
4 calls:
Slowest
36.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
15.0ms
(+ (* re re) (* im im))
13.0ms
(sqrt (+ (* re re) (* im im)))
9.0ms
(/ 1 (log base))

series524.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
293.0ms
(/ 1 (log base))
133.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
60.0ms
(sqrt (+ (* re re) (* im im)))
37.0ms
(+ (* re re) (* im im))

simplify3.7s

Counts
88 → 119
Calls
88 calls:
Slowest
602.0ms
(* (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base))))
409.0ms
(* (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (/ (* (* 1 1) 1) (* (* (log base) (log base)) (log base))))
307.0ms
(sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))
286.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
190.0ms
(* -1 (/ (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.6b

localize51.0ms

Local error

Found 4 expressions with local error:

31.0b
(log (+ (* re re) (* im im)))
0.4b
(/ (log base) (log (+ (* re re) (* im im))))
0.3b
(/ 1/2 (/ (log base) (log (+ (* re re) (* im im)))))
0.0b
(+ (* re re) (* im im))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
72×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
47×pow1
43×log-pow
24×associate-/r*
12×add-exp-log
11×add-cbrt-cube
7×associate-/l*
6×div-inv add-log-exp
4×cbrt-undiv div-exp insert-posit16
3×log-prod
2×log-div clear-num frac-2neg flip3-+ flip-+
1×+-commutative sum-log rem-log-exp associate-/r/
Counts
4 → 163
Calls
4 calls:
Slowest
13.0ms
(/ (log base) (log (+ (* re re) (* im im))))
13.0ms
(+ (* re re) (* im im))
12.0ms
(log (+ (* re re) (* im im)))
12.0ms
(/ 1/2 (/ (log base) (log (+ (* re re) (* im im)))))

series382.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(/ (log base) (log (+ (* re re) (* im im))))
142.0ms
(/ 1/2 (/ (log base) (log (+ (* re re) (* im im)))))
57.0ms
(log (+ (* re re) (* im im)))
33.0ms
(+ (* re re) (* im im))

simplify10.8s

Counts
206 → 175
Calls
206 calls:
Slowest
632.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))
550.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (/ (* (cbrt (log base)) (cbrt (log base))) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))))
434.0ms
(/ (* (* (log base) (log base)) (log base)) (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))))
416.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (/ (log base) (log (+ (* re re) (* im im)))) (/ (log base) (log (+ (* re re) (* im im))))) (/ (log base) (log (+ (* re re) (* im im))))))
392.0ms
(* -1/2 (/ (- (log -1) (log (/ -1 base))) (log (/ -1 re))))

prune2.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.6b

regimes529.0ms

Accuracy

59% (9.5b remaining)

Error of 16.9b against oracle of 7.4b and baseline of 30.6b

bsearch2.6s

end0.0ms

sample35.5s

Algorithm
intervals
Results
26.1s7787×body10240exit
5.5s15845×body80nan
2.8s8000×body80valid