Details

Time bar (total: 33.3s)

sample65.0ms

Algorithm
intervals
Results
50.0ms256×body80valid

simplify16.0ms

Calls
1 calls:
Slowest
16.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize39.0ms

Local error

Found 3 expressions with local error:

32.0b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt times-frac
14×*-un-lft-identity add-cube-cbrt
8×log-pow
7×pow1
5×add-cbrt-cube pow1/2 add-exp-log associate-/l* add-log-exp
4×sqrt-div
3×associate-/r* 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
21.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
6.0ms
(+ (* re re) (* im im))
5.0ms
(sqrt (+ (* re re) (* im im)))

series197.0ms

Calls
3 calls:
Slowest
143.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
40.0ms
(sqrt (+ (* re re) (* im im)))
14.0ms
(+ (* re re) (* im im))

simplify1.7s

Calls
55 calls:
Slowest
241.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
195.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
172.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
112.0ms
(* -1 (/ (log (/ 1 re)) (log 10)))
106.0ms
(/ (log (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (log 10))

prune833.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.3b

localize31.0ms

Local error

Found 4 expressions with local error:

33.2b
(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))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
38×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
28×associate-*r*
27×sqrt-prod
20×pow1
14×log-pow
12×add-exp-log
11×add-cbrt-cube
6×associate-/r* add-log-exp
4×log-div associate-*l* insert-posit16 associate-/l*
3×log-prod flip3-+ flip-+ div-inv
2×cbrt-undiv div-sub div-exp prod-exp cbrt-unprod
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
18.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
15.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
5.0ms
(+ (* re re) (* im im))
5.0ms
(log (+ (* re re) (* im im)))

series409.0ms

Calls
4 calls:
Slowest
202.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
143.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
43.0ms
(log (+ (* re re) (* im im)))
21.0ms
(+ (* re re) (* im im))

simplify4.5s

Calls
118 calls:
Slowest
715.0ms
(* (* (* (/ 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)))))
238.0ms
(+ (log (/ 1/2 (sqrt (log 10)))) (- (log (log (+ (* re re) (* im im)))) (log (sqrt (log 10)))))
234.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
233.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))
218.0ms
(/ (log (- (* (* re re) (* re re)) (* (* im im) (* im im)))) (sqrt (log 10)))

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.1b

localize15.0ms

Local error

Found 4 expressions with local error:

33.2b
(log (+ (* re re) (* im im)))
0.4b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (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))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
41×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
35×sqrt-prod
29×associate-*r*
25×pow1
21×add-exp-log
20×add-cbrt-cube
14×associate-*l* log-pow
10×sqrt-div
7×prod-exp cbrt-unprod
6×frac-times associate-/r* 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
20.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
17.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
10.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
2.0ms
(log (+ (* re re) (* im im)))

series926.0ms

Calls
4 calls:
Slowest
488.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
203.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
192.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
43.0ms
(log (+ (* re re) (* im im)))

simplify7.0s

Calls
146 calls:
Slowest
408.0ms
(* (* (* (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)))))
386.0ms
(* (* (* (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))))))
333.0ms
(* -2 (* (* (log (/ -1 re)) (sqrt 1/2)) (pow (/ 1 (pow (log 10) 3)) 1/4)))
327.0ms
(* -2 (* (pow (/ 1 (pow (log 10) 3)) 1/4) (* (log (/ 1 re)) (sqrt 1/2))))
325.0ms
(* -2 (/ (* (log (/ 1 re)) (pow (sqrt 1/2) 2)) (log 10)))

prune2.5s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.0b

localize8.0ms

Local error

Found 4 expressions with local error:

33.2b
(log (+ (* re re) (* im im)))
0.4b
(/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))) (sqrt (log 10)))
0.4b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))))
0.4b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
21×log-prod add-exp-log
20×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-cube-cbrt
15×distribute-rgt-in distribute-lft-in
14×associate-*l* sqrt-prod
13×pow1
9×sqrt-div
7×associate-*l/ prod-exp cbrt-unprod
6×associate-/r* times-frac
5×associate-*r*
4×pow-prod-down insert-posit16 add-log-exp
3×cbrt-undiv div-exp div-inv associate-/l/
2×frac-times log-div associate-*r/ log-pow *-commutative
1×clear-num frac-2neg flip3-+ rem-log-exp flip-+ associate-/l*
Calls
4 calls:
Slowest
38.0ms
(/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))) (sqrt (log 10)))
25.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))))
16.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))
2.0ms
(log (+ (* re re) (* im im)))

series860.0ms

Calls
4 calls:
Slowest
342.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))
249.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))))
223.0ms
(/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))) (sqrt (log 10)))
45.0ms
(log (+ (* re re) (* im im)))

simplify8.0s

Calls
95 calls:
Slowest
622.0ms
(* 2 (* (* (log im) (pow (sqrt 1/2) 2)) (sqrt (/ 1 (log 10)))))
538.0ms
(* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))))
448.0ms
(/ (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
414.0ms
(* (* (* (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))))))
376.0ms
(/ (* (* (* (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))))

prune1.6s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 8.0b

regimes1.0s

Accuracy

56.7% (10.3b remaining)

Error of 17.4b against oracle of 7.1b and baseline of 31.0b

bsearch184.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.3s8000×body80valid