Details

Time bar (total: 36.3s)

sample30.0ms

Algorithm
intervals
Results
22.0ms256×body80valid

simplify9.0ms

Calls
1 calls:
Slowest
9.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize18.0ms

Local error

Found 3 expressions with local error:

29.4b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite24.0ms

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
18.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
3.0ms
(+ (* re re) (* im im))
2.0ms
(sqrt (+ (* re re) (* im im)))

series200.0ms

Calls
3 calls:
Slowest
164.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
22.0ms
(sqrt (+ (* re re) (* im im)))
14.0ms
(+ (* re re) (* im im))

simplify1.8s

Calls
55 calls:
Slowest
238.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
216.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
190.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
152.0ms
(* -1 (/ (log (/ 1 re)) (log 10)))
140.0ms
(* -1 (/ (log (/ -1 re)) (log 10)))

prune958.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.2b

localize13.0ms

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))

rewrite23.0ms

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
9.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
8.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
3.0ms
(+ (* re re) (* im im))
2.0ms
(log (+ (* re re) (* im im)))

series365.0ms

Calls
4 calls:
Slowest
169.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
144.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
38.0ms
(log (+ (* re re) (* im im)))
14.0ms
(+ (* re re) (* im im))

simplify4.4s

Calls
118 calls:
Slowest
704.0ms
(* (* (* (/ 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)))))
231.0ms
(/ (log (- (* (* re re) (* re re)) (* (* im im) (* im im)))) (sqrt (log 10)))
215.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
207.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))
190.0ms
(+ (log (/ 1/2 (sqrt (log 10)))) (- (log (log (+ (* re re) (* im im)))) (log (sqrt (log 10)))))

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.0b

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

rewrite49.0ms

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
17.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
13.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
12.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
4.0ms
(log (+ (* re re) (* im im)))

series961.0ms

Calls
4 calls:
Slowest
493.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
232.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
190.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
45.0ms
(log (+ (* re re) (* im im)))

simplify6.9s

Calls
146 calls:
Slowest
399.0ms
(* (* (* (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)))))
388.0ms
(* -2 (* (pow (/ 1 (pow (log 10) 3)) 1/4) (* (log (/ 1 re)) (sqrt 1/2))))
300.0ms
(* -2 (/ (* (log (/ 1 re)) (pow (sqrt 1/2) 2)) (log 10)))
287.0ms
(* (* (* (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))))))
276.0ms
(* -2 (* (* (log (/ -1 re)) (sqrt 1/2)) (pow (/ 1 (pow (log 10) 3)) 1/4)))

prune2.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

localize15.0ms

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

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
31×sqrt-prod
29×pow1 associate-*r*
26×add-exp-log
25×add-cbrt-cube
14×log-pow
13×associate-*r/
11×prod-exp cbrt-unprod
10×sqrt-div associate-*l*
7×pow-prod-down
6×frac-times associate-/r*
4×log-div associate-*l/ insert-posit16 associate-/l* add-log-exp
3×cbrt-undiv log-prod div-exp div-inv
2×flip3-+ div-sub *-commutative flip-+
1×clear-num frac-2neg rem-log-exp
Calls
4 calls:
Slowest
35.0ms
(* (sqrt 1/2) (* (sqrt (/ 1 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))))
21.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
9.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
4.0ms
(log (+ (* re re) (* im im)))

series911.0ms

Calls
4 calls:
Slowest
496.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
200.0ms
(* (sqrt 1/2) (* (sqrt (/ 1 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))))
174.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
40.0ms
(log (+ (* re re) (* im im)))

simplify9.9s

Calls
142 calls:
Slowest
889.0ms
(* (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* (* (sqrt (/ 1 (sqrt (log 10)))) (sqrt (/ 1 (sqrt (log 10))))) (sqrt (/ 1 (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)))))))
534.0ms
(* (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* (* (sqrt (/ 1 (sqrt (log 10)))) (sqrt (/ 1 (sqrt (log 10))))) (sqrt (/ 1 (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 (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))))
498.0ms
(+ (log (sqrt 1/2)) (+ (log (sqrt (/ 1 (sqrt (log 10))))) (+ (log (sqrt (/ 1/2 (sqrt (log 10))))) (log (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))))
441.0ms
(* (* (* (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)))))
431.0ms
(* (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* (* (sqrt (/ 1 (sqrt (log 10)))) (sqrt (/ 1 (sqrt (log 10))))) (sqrt (/ 1 (sqrt (log 10))))) (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))))

prune2.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

regimes833.0ms

Accuracy

57.7% (10.0b remaining)

Error of 17.3b against oracle of 7.3b and baseline of 30.9b

bsearch344.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.2s8000×body80valid