Details

Time bar (total: 37.1s)

sample56.0ms

Algorithm
intervals
Results
42.0ms256×body80valid

simplify19.0ms

Calls
1 calls:
Slowest
19.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize18.0ms

Local error

Found 3 expressions with local error:

31.4b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite77.0ms

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
Calls
3 calls:
Slowest
57.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
13.0ms
(+ (* re re) (* im im))
6.0ms
(sqrt (+ (* re re) (* im im)))

series253.0ms

Calls
3 calls:
Slowest
165.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
45.0ms
(sqrt (+ (* re re) (* im im)))
42.0ms
(+ (* re re) (* im im))

simplify2.7s

Calls
76 calls:
Slowest
429.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
282.0ms
(sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))
280.0ms
(/ (log (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (log 10))
240.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
186.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune943.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.8b

localize23.0ms

Local error

Found 4 expressions with local error:

32.6b
(log (+ (* re re) (* im im)))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.2b
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.0b
(+ (* re re) (* im im))

rewrite72.0ms

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
Calls
4 calls:
Slowest
24.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
22.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
14.0ms
(+ (* re re) (* im im))
5.0ms
(log (+ (* re re) (* im im)))

series645.0ms

Calls
4 calls:
Slowest
286.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
226.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
86.0ms
(log (+ (* re re) (* im im)))
47.0ms
(+ (* re re) (* im im))

simplify8.7s

Calls
174 calls:
Slowest
848.0ms
(* (* (* (/ 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)))))
436.0ms
(* (/ (* (* 1/2 1/2) 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)))))
421.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
371.0ms
(* (/ (* (* 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)))))
342.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.6b

localize55.0ms

Local error

Found 4 expressions with local error:

32.6b
(log (+ (* re re) (* im im)))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.3b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.3b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
126×sqrt-prod
112×times-frac
107×add-sqr-sqrt
69×*-un-lft-identity add-cube-cbrt
56×associate-*l*
42×pow1
33×associate-*r*
31×log-pow
21×add-exp-log
20×add-cbrt-cube
12×unswap-sqr
10×sqrt-div
7×associate-/r* prod-exp cbrt-unprod
6×frac-times associate-*r/
4×log-div pow-prod-down associate-*l/ insert-posit16 div-inv associate-/l* add-log-exp
3×cbrt-undiv log-prod div-exp
2×flip3-+ div-sub *-commutative flip-+
1×clear-num frac-2neg rem-log-exp
Calls
4 calls:
Slowest
67.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
23.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
19.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
7.0ms
(log (+ (* re re) (* im im)))

series1.4s

Calls
4 calls:
Slowest
696.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
310.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
309.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
78.0ms
(log (+ (* re re) (* im im)))

simplify11.5s

Calls
225 calls:
Slowest
871.0ms
(* (* (* (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)))))
396.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
393.0ms
(* -2 (/ (* (log (/ 1 re)) (pow (sqrt 1/2) 2)) (log 10)))
392.0ms
(* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (* (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))))))
369.0ms
(* -2 (* (* (log (/ -1 re)) (sqrt 1/2)) (pow (/ 1 (pow (log 10) 3)) 1/4)))

prune3.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.5b

localize61.0ms

Local error

Found 4 expressions with local error:

32.6b
(log (+ (* re re) (* im im)))
1.6b
(* (cbrt (log 10)) (cbrt (log 10)))
1.0b
(cbrt (log 10))
1.0b
(cbrt (log 10))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod
23×add-sqr-sqrt
20×pow1
17×*-un-lft-identity
15×add-cube-cbrt
9×swap-sqr log-pow
8×pow1/3
7×associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
3×log-prod
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-+
Calls
4 calls:
Slowest
8.0ms
(* (cbrt (log 10)) (cbrt (log 10)))
6.0ms
(log (+ (* re re) (* im im)))
1.0ms
(cbrt (log 10))
1.0ms
(cbrt (log 10))

series55.0ms

Calls
4 calls:
Slowest
54.0ms
(log (+ (* re re) (* im im)))
0.0ms
(* (cbrt (log 10)) (cbrt (log 10)))
0.0ms
(cbrt (log 10))
0.0ms
(cbrt (log 10))

simplify1.3s

Calls
72 calls:
Slowest
296.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))
256.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))
102.0ms
(- (* 2 (log (/ -1 re))))
89.0ms
(* (* (cbrt (cbrt (log 10))) (cbrt (cbrt (log 10)))) (* (cbrt (cbrt (log 10))) (cbrt (cbrt (log 10)))))
23.0ms
(- (* 2 (log (/ 1 re))))

prune1.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.5b

regimes824.0ms

Accuracy

58.8% (9.6b remaining)

Error of 16.9b against oracle of 7.3b and baseline of 30.6b

bsearch278.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.2s8000×body80valid