Details

Time bar (total: 1.3m)

sample1.6s

Algorithm
intervals
Results
1.3s266×body10240exit
157.0ms478×body80nan
93.0ms256×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: 28.8b

localize65.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* re re) (* im im)))
0.5b
(* (log base) (log base))
0.4b
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
0.3b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))

rewrite73.0ms

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
31.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
14.0ms
(* (log base) (log base))
14.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
12.0ms
(sqrt (+ (* re re) (* im im)))

series536.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
225.0ms
(* (log base) (log base))
162.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
95.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
54.0ms
(sqrt (+ (* re re) (* im im)))

simplify6.5s

Counts
83 → 116
Calls
83 calls:
Slowest
733.0ms
(/ (* (* (* (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))))
620.0ms
(/ (* (* (* (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))))
543.0ms
(/ (* (* (* (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))))
488.0ms
(- (+ (log (log (sqrt (+ (* re re) (* im im))))) (log (log base))) (+ (log (log base)) (log (log base))))
483.0ms
(/ (* (* (* (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))))

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

localize40.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* re re) (* im im)))
0.5b
(* (log base) (log base))
0.3b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b
(/ (* (log base) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))

rewrite46.0ms

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
16.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms
(/ (* (log base) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
7.0ms
(* (log base) (log base))
6.0ms
(sqrt (+ (* re re) (* im im)))

series610.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
230.0ms
(* (log base) (log base))
205.0ms
(/ (* (log base) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
132.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
43.0ms
(sqrt (+ (* re re) (* im im)))

simplify7.5s

Counts
83 → 116
Calls
83 calls:
Slowest
879.0ms
(/ (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))) (* (* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (* (log (sqrt (+ (* re re) (* im im)))) (log base))))
751.0ms
(/ (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))) (* (* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (* (log (sqrt (+ (* re re) (* im im)))) (log base))))
606.0ms
(* -1 (/ (- (log -1) (log (/ -1 base))) (log (/ -1 re))))
572.0ms
(- (log (* (log base) (log base))) (+ (log (log (sqrt (+ (* re re) (* im im))))) (log (log base))))
517.0ms
(/ (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))) (* (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log base) (log base)) (log base))))

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

localize50.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* re re) (* im im)))
0.5b
(* (log base) (log base))
0.4b
(* (* (log base) (log base)) (/ 1 (* (log (sqrt (+ (* re re) (* im im)))) (log base))))
0.3b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
53×add-exp-log
29×add-cbrt-cube prod-exp
28×pow1
23×add-sqr-sqrt
19×*-un-lft-identity
17×add-cube-cbrt
15×associate-*r*
13×cbrt-unprod
12×log-prod
11×associate-*l*
10×log-pow
8×div-exp
6×distribute-rgt-in distribute-lft-in swap-sqr
5×pow-prod-down
4×cbrt-undiv rec-exp 1-exp insert-posit16 add-log-exp
3×times-frac *-commutative sqrt-prod unswap-sqr
2×sqrt-pow1 pow1/2 sqrt-div
1×pow2 rem-sqrt-square flip3-+ pow-plus associate-*r/ pow-sqr un-div-inv pow-prod-up flip-+ div-inv
Counts
4 → 124
Calls
4 calls:
Slowest
48.0ms
(* (* (log base) (log base)) (/ 1 (* (log (sqrt (+ (* re re) (* im im)))) (log base))))
24.0ms
(* (log base) (log base))
12.0ms
(sqrt (+ (* re re) (* im im)))
11.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))

series623.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
212.0ms
(* (* (log base) (log base)) (/ 1 (* (log (sqrt (+ (* re re) (* im im)))) (log base))))
205.0ms
(* (log base) (log base))
161.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
45.0ms
(sqrt (+ (* re re) (* im im)))

simplify14.5s

Counts
105 → 136
Calls
105 calls:
Slowest
1.4s
(+ (log (* (log base) (log base))) (log (/ 1 (* (log (sqrt (+ (* re re) (* im im)))) (log base)))))
899.0ms
(+ (+ (log (log base)) (log (log base))) (log (/ 1 (* (log (sqrt (+ (* re re) (* im im)))) (log base)))))
744.0ms
(+ (+ (log (log base)) (log (log base))) (- (log (* (log (sqrt (+ (* re re) (* im im)))) (log base)))))
699.0ms
(+ (+ (log (log base)) (log (log base))) (- 0 (log (* (log (sqrt (+ (* re re) (* im im)))) (log base)))))
668.0ms
(+ (log (* (log base) (log base))) (- 0 (log (* (log (sqrt (+ (* re re) (* im im)))) (log base)))))

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.9b

localize67.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* re re) (* im im)))
0.6b
(cbrt base)
0.6b
(cbrt base)
0.6b
(cbrt base)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 52
Calls
4 calls:
Slowest
12.0ms
(sqrt (+ (* re re) (* im im)))
2.0ms
(cbrt base)
1.0ms
(cbrt base)
1.0ms
(cbrt base)

series903.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
299.0ms
(cbrt base)
279.0ms
(cbrt base)
275.0ms
(cbrt base)
50.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts
28 → 64
Calls
28 calls:
Slowest
367.0ms
(sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))
252.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
146.0ms
(* (cbrt -1) (pow (* base -1) 1/3))
129.0ms
(* (cbrt -1) (pow (* base -1) 1/3))
94.0ms
(* (cbrt -1) (pow (* base -1) 1/3))

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.8b

regimes788.0ms

Accuracy

59.3% (9.4b remaining)

Error of 16.9b against oracle of 7.5b and baseline of 30.6b

bsearch2.0s

end0.0ms

sample36.4s

Algorithm
intervals
Results
28.0s8072×body10240exit
4.9s16139×body80nan
2.6s8000×body80valid