Details

Time bar (total: 34.4s)

sample39.0ms

Algorithm
intervals
Results
29.0ms256×body80valid

simplify14.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize41.0ms

Local error

Found 3 expressions with local error:

29.6b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite21.0ms

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
12.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
5.0ms
(sqrt (+ (* re re) (* im im)))
3.0ms
(+ (* re re) (* im im))

series192.0ms

Calls
3 calls:
Slowest
149.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
28.0ms
(sqrt (+ (* re re) (* im im)))
15.0ms
(+ (* re re) (* im im))

simplify1.6s

Calls
55 calls:
Slowest
190.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
186.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
171.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
111.0ms
(* -1 (/ (log (/ 1 re)) (log 10)))
108.0ms
(/ (log (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (log 10))

prune881.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.5b

localize30.0ms

Local error

Found 4 expressions with local error:

30.6b
(log (+ (* re re) (* im im)))
0.5b
(/ (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))

rewrite29.0ms

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
11.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
8.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
5.0ms
(log (+ (* re re) (* im im)))
3.0ms
(+ (* re re) (* im im))

series395.0ms

Calls
4 calls:
Slowest
182.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
150.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
48.0ms
(log (+ (* re re) (* im im)))
15.0ms
(+ (* re re) (* im im))

simplify4.3s

Calls
118 calls:
Slowest
662.0ms
(* (* (* (/ 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)))))
246.0ms
(* (* (* (/ 1/2 (sqrt (log 10))) (/ 1/2 (sqrt (log 10)))) (/ 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)))))
228.0ms
(+ (log (/ 1/2 (sqrt (log 10)))) (- (log (log (+ (* re re) (* im im)))) (log (sqrt (log 10)))))
216.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
191.0ms
(/ (log (- (* (* re re) (* re re)) (* (* im im) (* im im)))) (sqrt (log 10)))

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.3b

localize16.0ms

Local error

Found 4 expressions with local error:

30.6b
(log (+ (* re re) (* im im)))
0.5b
(/ (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))) (sqrt (log 10)))))
0.4b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))

rewrite83.0ms

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
36.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
22.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
18.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
4.0ms
(log (+ (* re re) (* im im)))

series1.0s

Calls
4 calls:
Slowest
581.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
224.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
195.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
45.0ms
(log (+ (* re re) (* im im)))

simplify6.8s

Calls
146 calls:
Slowest
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))))))
386.0ms
(* (* (* (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)))))
362.0ms
(* -2 (* (* (log (/ -1 re)) (sqrt 1/2)) (pow (/ 1 (pow (log 10) 3)) 1/4)))
345.0ms
(* -2 (* (pow (/ 1 (pow (log 10) 3)) 1/4) (* (log (/ 1 re)) (sqrt 1/2))))
317.0ms
(* -2 (/ (* (log (/ 1 re)) (pow (sqrt 1/2) 2)) (log 10)))

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 4 expressions with local error:

30.6b
(log (+ (* re re) (* im im)))
1.0b
(sqrt (sqrt (log 10)))
0.5b
(/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt 1/2) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))) (sqrt (sqrt (log 10))))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
43×sqrt-prod
33×times-frac
32×add-sqr-sqrt
30×*-un-lft-identity add-cube-cbrt
21×add-exp-log
20×add-cbrt-cube
15×associate-/r*
12×pow1
8×log-pow
6×cbrt-undiv div-exp
5×prod-exp cbrt-unprod associate-/l*
4×log-div insert-posit16 add-log-exp
3×log-prod associate-*r/ associate-/l/
2×rem-sqrt-square clear-num frac-2neg flip3-+ sqrt-div div-sub flip-+ div-inv
1×frac-times pow1/2 rem-log-exp associate-*l/
Calls
4 calls:
Slowest
27.0ms
(/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt 1/2) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))) (sqrt (sqrt (log 10))))
17.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
2.0ms
(log (+ (* re re) (* im im)))
1.0ms
(sqrt (sqrt (log 10)))

series403.0ms

Calls
4 calls:
Slowest
191.0ms
(/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt 1/2) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))) (sqrt (sqrt (log 10))))
170.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
41.0ms
(log (+ (* re re) (* im im)))
0.0ms
(sqrt (sqrt (log 10)))

simplify8.9s

Calls
123 calls:
Slowest
845.0ms
(/ (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))))) (* (* (sqrt (sqrt (log 10))) (sqrt (sqrt (log 10)))) (sqrt (sqrt (log 10)))))
819.0ms
(/ (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))) (* (* (sqrt (sqrt (log 10))) (sqrt (sqrt (log 10)))) (sqrt (sqrt (log 10)))))
638.0ms
(/ (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (* (sqrt 1/2) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (* (sqrt 1/2) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))) (* (sqrt 1/2) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))) (* (* (sqrt (sqrt (log 10))) (sqrt (sqrt (log 10)))) (sqrt (sqrt (log 10)))))
616.0ms
(/ (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt 1/2) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt 1/2) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt 1/2) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))) (* (* (sqrt (sqrt (log 10))) (sqrt (sqrt (log 10)))) (sqrt (sqrt (log 10)))))
467.0ms
(- (+ (log (sqrt (/ 1/2 (sqrt (log 10))))) (+ (log (sqrt 1/2)) (log (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))) (log (sqrt (sqrt (log 10)))))

prune2.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.2b

regimes1.5s

Accuracy

55.6% (10.6b remaining)

Error of 17.9b against oracle of 7.2b and baseline of 31.2b

bsearch165.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.2s8000×body80valid