Details

Time bar (total: 1.6m)

sample1.1s

Algorithm
intervals
Results
867.0ms295×body10240exit
114.0ms256×body80valid
111.0ms520×body80nan

simplify28.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
28.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize55.0ms

Local error

Found 4 expressions with local error:

26.3b
(sqrt (+ (* re re) (* im im)))
0.5b
(* (log base) (log base))
0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))

rewrite74.0ms

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
39.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
19.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
7.0ms
(* (log base) (log base))
6.0ms
(sqrt (+ (* re re) (* im im)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(* (log base) (log base))
120.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
113.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
67.0ms
(sqrt (+ (* re re) (* im im)))

simplify14.0s

Counts
138 → 116
Calls
138 calls:
Slowest
1.2s
(* (* (/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base))) (/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))) (/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base))))
810.0ms
(log (/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base))))
646.0ms
(/ (* (* (* (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))))
630.0ms
(sqrt (+ (* (* re re) (* re re)) (- (* (* im im) (* im im)) (* (* re re) (* im im)))))
573.0ms
(sqrt (/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base))))

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (log (/ -1 re)) (log base))
0.0b
(log (/ -1 re))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
25×times-frac
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×pow1 log-prod
11×log-pow
7×add-exp-log
4×associate-/r* add-cbrt-cube associate-/l*
2×log-div div-exp rem-log-exp insert-posit16 div-inv add-log-exp
1×cbrt-undiv clear-num frac-2neg div-sub
Counts
2 → 63
Calls
2 calls:
Slowest
14.0ms
(/ (log (/ -1 re)) (log base))
4.0ms
(log (/ -1 re))

series303.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
178.0ms
(log (/ -1 re))
124.0ms
(/ (log (/ -1 re)) (log base))

simplify4.1s

Counts
99 → 69
Calls
99 calls:
Slowest
478.0ms
(* (* (/ (log (/ -1 re)) (log base)) (/ (log (/ -1 re)) (log base))) (/ (log (/ -1 re)) (log base)))
374.0ms
(* (* (log (/ -1 re)) (log (/ -1 re))) (log (/ -1 re)))
275.0ms
(* -1 (/ (+ (log (/ 1 re)) (log -1)) (log (/ 1 base))))
173.0ms
(/ (* (* (log (/ -1 re)) (log (/ -1 re))) (log (/ -1 re))) (* (* (log base) (log base)) (log base)))
116.0ms
(log (/ (* (cbrt -1) (cbrt -1)) (* (cbrt re) (cbrt re))))

prune701.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt re)
0.6b
(cbrt re)
0.6b
(cbrt re)
0.5b
(* (/ (cbrt -1) (cbrt re)) (/ (cbrt -1) (cbrt re)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
197×add-sqr-sqrt
193×cbrt-prod
184×times-frac
107×*-un-lft-identity add-cube-cbrt
40×swap-sqr associate-*r* associate-*l*
25×unswap-sqr
16×add-exp-log
11×pow1
8×add-cbrt-cube
4×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 div-inv add-log-exp
3×pow1/3
1×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 206
Calls
4 calls:
Slowest
17.0ms
(* (/ (cbrt -1) (cbrt re)) (/ (cbrt -1) (cbrt re)))
1.0ms
(cbrt re)
1.0ms
(cbrt re)
1.0ms
(cbrt re)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
293.0ms
(* (/ (cbrt -1) (cbrt re)) (/ (cbrt -1) (cbrt re)))
245.0ms
(cbrt re)
245.0ms
(cbrt re)
244.0ms
(cbrt re)

simplify19.4s

Counts
288 → 218
Calls
288 calls:
Slowest
492.0ms
(* (pow (/ 1 (pow re 2)) 1/3) (pow (cbrt -1) 2))
476.0ms
(* (/ (cbrt (sqrt -1)) (sqrt (cbrt re))) (/ (cbrt -1) (cbrt re)))
406.0ms
(* (pow (/ 1 (pow re 2)) 1/3) (pow (cbrt -1) 2))
404.0ms
(* (/ (cbrt -1) (cbrt re)) (/ (cbrt 1) (* (cbrt (cbrt re)) (cbrt (cbrt re)))))
354.0ms
(* (/ (cbrt -1) (cbrt re)) (/ 1 (* (cbrt (cbrt re)) (cbrt (cbrt re)))))

prune2.8s

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 6.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.5b
(* (log base) (log base))
0.4b
(/ (* (log (- re)) (log base)) (* (log base) (log base)))
0.4b
(* (log (- re)) (log base))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1
19×add-cbrt-cube add-exp-log
17×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
12×log-prod
8×associate-*r* associate-*l* log-pow
6×distribute-rgt-in distribute-lft-in swap-sqr prod-exp cbrt-unprod
4×cbrt-undiv div-exp
3×insert-posit16 add-log-exp
2×pow-prod-down *-commutative unswap-sqr
1×pow2 clear-num associate-/r* frac-2neg times-frac pow-plus pow-sqr pow-prod-up div-inv associate-/l*
Counts
3 → 86
Calls
3 calls:
Slowest
20.0ms
(* (log base) (log base))
13.0ms
(/ (* (log (- re)) (log base)) (* (log base) (log base)))
8.0ms
(* (log (- re)) (log base))

series484.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
252.0ms
(* (log base) (log base))
123.0ms
(/ (* (log (- re)) (log base)) (* (log base) (log base)))
109.0ms
(* (log (- re)) (log base))

simplify12.3s

Counts
114 → 95
Calls
114 calls:
Slowest
1.1s
(* (* (/ (* (log (- re)) (log base)) (* (log base) (log base))) (/ (* (log (- re)) (log base)) (* (log base) (log base)))) (/ (* (log (- re)) (log base)) (* (log base) (log base))))
992.0ms
(/ (* (log base) (log base)) (* (log (- re)) (log base)))
660.0ms
(* (cbrt (/ (* (log (- re)) (log base)) (* (log base) (log base)))) (cbrt (/ (* (log (- re)) (log base)) (* (log base) (log base)))))
562.0ms
(/ (* (* (* (log (- re)) (log base)) (* (log (- re)) (log base))) (* (log (- re)) (log base))) (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))))
551.0ms
(log (/ (* (log (- re)) (log base)) (* (log base) (log base))))

prune933.0ms

Pruning

24 alts after pruning (22 fresh and 2 done)

Merged error: 6.0b

regimes1.3s

Accuracy

55.7% (9.7b remaining)

Error of 16.9b against oracle of 7.2b and baseline of 29.1b

bsearch214.0ms

end0.0ms

sample36.8s

Algorithm
intervals
Results
28.5s8162×body10240exit
5.2s15928×body80nan
2.0s8000×body80valid