Details

Time bar (total: 41.4s)

sample31.0ms

Algorithm
intervals
Results
22.0ms256×body80valid

simplify13.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
13.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize40.0ms

Local error

Found 3 expressions with local error:

24.8b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite61.0ms

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
34.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
13.0ms
(+ (* re re) (* im im))
11.0ms
(sqrt (+ (* re re) (* im im)))

series323.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
226.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
66.0ms
(sqrt (+ (* re re) (* im im)))
32.0ms
(+ (* re re) (* im im))

simplify3.1s

Counts
76 → 86
Calls
76 calls:
Slowest
434.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
368.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
308.0ms
(sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))
283.0ms
(/ (log (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (log 10))
256.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune904.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.4b

localize29.0ms

Local error

Found 4 expressions with local error:

25.9b
(log (+ (* re re) (* im im)))
0.4b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.3b
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.0b
(+ (* re re) (* im im))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
83×add-sqr-sqrt
54×sqrt-prod
53×*-un-lft-identity add-cube-cbrt
34×pow1
32×associate-*r*
28×log-pow
25×associate-*l*
19×add-exp-log
18×add-cbrt-cube
9×unswap-sqr
7×associate-/r*
6×add-log-exp
5×cbrt-undiv div-exp
4×log-div prod-exp cbrt-unprod insert-posit16 associate-/l*
3×log-prod flip3-+ flip-+ div-inv
2×div-sub
1×frac-times +-commutative clear-num sum-log frac-2neg rem-log-exp pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 168
Calls
4 calls:
Slowest
39.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
39.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
17.0ms
(log (+ (* re re) (* im im)))
14.0ms
(+ (* re re) (* im im))

series636.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
291.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
224.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
78.0ms
(log (+ (* re re) (* im im)))
43.0ms
(+ (* re re) (* im im))

simplify8.5s

Counts
174 → 180
Calls
174 calls:
Slowest
869.0ms
(* (* (* (/ 1/2 (sqrt (log 10))) (/ 1/2 (sqrt (log 10)))) (/ 1/2 (sqrt (log 10)))) (* (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
401.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
348.0ms
(/ (log (+ (pow (* re re) 3) (pow (* im im) 3))) (sqrt (log 10)))
335.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))
315.0ms
(* (/ (* (* 1/2 1/2) 1/2) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))) (* (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize58.0ms

Local error

Found 4 expressions with local error:

25.9b
(log (+ (* re re) (* im im)))
1.0b
(cbrt (log 10))
1.0b
(cbrt (log 10))
1.0b
(* (cbrt 1/2) (cbrt 1/2))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
14×pow1
8×pow1/3
7×add-exp-log
6×swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
3×log-prod log-pow
2×log-div pow-prod-down pow-sqr pow-prod-up
1×pow2 flip3-+ pow-plus rem-log-exp prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 82
Calls
4 calls:
Slowest
14.0ms
(* (cbrt 1/2) (cbrt 1/2))
10.0ms
(log (+ (* re re) (* im im)))
2.0ms
(cbrt (log 10))
1.0ms
(cbrt (log 10))

series77.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
76.0ms
(log (+ (* re re) (* im im)))
0.0ms
(cbrt (log 10))
0.0ms
(* (cbrt 1/2) (cbrt 1/2))
0.0ms
(cbrt (log 10))

simplify1.8s

Counts
62 → 88
Calls
62 calls:
Slowest
340.0ms
(* (/ (* (cbrt 1/2) (cbrt 1/2)) (fabs (cbrt (log 10)))) (* (/ (cbrt 1/2) (sqrt (cbrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
271.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))
249.0ms
(* (/ (* (cbrt 1/2) (cbrt 1/2)) (fabs (cbrt (log 10)))) (* (/ (cbrt 1/2) (sqrt (cbrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
245.0ms
(* (/ (* (cbrt 1/2) (cbrt 1/2)) (fabs (cbrt (log 10)))) (* (/ (cbrt 1/2) (sqrt (cbrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
233.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

localize33.0ms

Local error

Found 4 expressions with local error:

25.9b
(log (+ (* re re) (* im im)))
0.5b
(* (sqrt 1/2) (* (/ (sqrt 1/2) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
0.4b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.3b
(* (/ (sqrt 1/2) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
120×add-sqr-sqrt times-frac
101×sqrt-prod
68×*-un-lft-identity add-cube-cbrt
52×associate-*l*
42×pow1
37×add-exp-log
36×add-cbrt-cube
33×associate-*r*
31×log-pow
15×unswap-sqr
13×prod-exp cbrt-unprod
9×cbrt-undiv div-exp
7×associate-/r*
5×associate-*r/
4×log-div pow-prod-down insert-posit16 associate-/l* add-log-exp
3×log-prod div-inv
2×frac-times flip3-+ div-sub associate-*l/ *-commutative flip-+
1×clear-num frac-2neg rem-log-exp
Counts
4 → 214
Calls
4 calls:
Slowest
50.0ms
(* (sqrt 1/2) (* (/ (sqrt 1/2) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
33.0ms
(* (/ (sqrt 1/2) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
20.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
5.0ms
(log (+ (* re re) (* im im)))

series804.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
276.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
255.0ms
(* (sqrt 1/2) (* (/ (sqrt 1/2) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
204.0ms
(* (/ (sqrt 1/2) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
67.0ms
(log (+ (* re re) (* im im)))

simplify15.4s

Counts
228 → 226
Calls
228 calls:
Slowest
656.0ms
(* (* (* (/ (sqrt 1/2) (sqrt (log 10))) (/ (sqrt 1/2) (sqrt (log 10)))) (/ (sqrt 1/2) (sqrt (log 10)))) (* (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
547.0ms
(* (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (/ (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))) (* (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))))
545.0ms
(* (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (/ (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))) (/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))))
493.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
457.0ms
(* (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* (* (/ (sqrt 1/2) (sqrt (log 10))) (/ (sqrt 1/2) (sqrt (log 10)))) (/ (sqrt 1/2) (sqrt (log 10)))) (/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))))

prune2.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.2b

regimes910.0ms

Accuracy

59.2% (9.7b remaining)

Error of 17.2b against oracle of 7.5b and baseline of 31.2b

bsearch188.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.6s8000×body80valid