Details

Time bar (total: 50.7s)

sample58.0ms

Algorithm
intervals
Results
43.0ms256×body80valid

simplify31.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
31.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
20×pow1
16×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
6×sqrt-pow1 pow1/2 associate-/l*
4×associate-/r* add-cbrt-cube sqrt-div add-exp-log
3×sqrt-prod
2×log-div flip3-+ div-sub flip-+ insert-posit16 add-log-exp
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg div-exp div-inv
Counts
2 → 65
Calls
2 calls:
Slowest
34.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
9.0ms
(sqrt (+ (* re re) (* im im)))

series251.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
192.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
58.0ms
(sqrt (+ (* re re) (* im im)))

simplify3.0s

Counts
72 → 71
Calls
72 calls:
Slowest
446.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
378.0ms
(sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))
366.0ms
(/ (log (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (log 10))
267.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
232.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune920.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize34.0ms

Local error

Found 3 expressions with local error:

30.9b
(log (+ (* re re) (* im im)))
0.4b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.2b
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
82×add-sqr-sqrt
54×sqrt-prod
52×*-un-lft-identity add-cube-cbrt
33×pow1
32×associate-*r*
28×log-pow
25×associate-*l*
18×add-exp-log
17×add-cbrt-cube
9×unswap-sqr
7×associate-/r*
5×cbrt-undiv div-exp
4×log-div prod-exp cbrt-unprod associate-/l*
3×log-prod insert-posit16 div-inv add-log-exp
2×flip3-+ div-sub flip-+
1×frac-times clear-num frac-2neg rem-log-exp pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
3 → 156
Calls
3 calls:
Slowest
45.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
38.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
12.0ms
(log (+ (* re re) (* im im)))

series485.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
241.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
178.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
66.0ms
(log (+ (* re re) (* im im)))

simplify8.9s

Counts
170 → 165
Calls
170 calls:
Slowest
872.0ms
(* (* (* (/ 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)))))
462.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
381.0ms
(* (/ (* (* 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)))))
333.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))
324.0ms
(/ (log (+ (pow (* re re) 3) (pow (* im im) 3))) (sqrt (log 10)))

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.0b

localize36.0ms

Local error

Found 4 expressions with local error:

30.9b
(log (+ (* re re) (* im im)))
0.4b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.4b
(* (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))) (sqrt (log 10)))))

rewrite154.0ms

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
Counts
4 → 211
Calls
4 calls:
Slowest
77.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
38.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
29.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
7.0ms
(log (+ (* re re) (* im im)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
674.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
342.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
242.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
74.0ms
(log (+ (* re re) (* im im)))

simplify12.4s

Counts
225 → 223
Calls
225 calls:
Slowest
686.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))
557.0ms
(* (* (* (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)))))
542.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
420.0ms
(* -2 (/ (* (log (/ 1 re)) (pow (sqrt 1/2) 2)) (log 10)))
413.0ms
(* (* (* (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))))))

prune3.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

localize42.0ms

Local error

Found 4 expressions with local error:

30.9b
(log (+ (* re re) (* im im)))
0.4b
(/ (* (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)))) (sqrt (log 10))))
0.3b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
94×sqrt-prod
65×add-sqr-sqrt
60×times-frac
56×associate-*l*
45×*-un-lft-identity add-cube-cbrt
21×add-exp-log
20×add-cbrt-cube
19×pow1
15×associate-*r*
11×log-pow
9×log-prod
8×unswap-sqr
7×associate-/r*
6×prod-exp cbrt-unprod
4×cbrt-undiv sqrt-div div-exp insert-posit16 div-inv add-log-exp
3×distribute-rgt-in distribute-lft-in associate-*l/
2×log-div pow-prod-down *-commutative
1×frac-times clear-num frac-2neg flip3-+ rem-log-exp associate-*r/ flip-+ associate-/l* associate-/l/
Counts
4 → 163
Calls
4 calls:
Slowest
62.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))) (sqrt (log 10))))
49.0ms
(/ (* (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))))
7.0ms
(log (+ (* re re) (* im im)))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
763.0ms
(/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))) (sqrt (log 10)))
494.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im))))
325.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (* (sqrt (/ 1/2 (sqrt (log 10)))) (log (+ (* re re) (* im im)))) (sqrt (log 10))))
76.0ms
(log (+ (* re re) (* im im)))

simplify10.0s

Counts
151 → 175
Calls
151 calls:
Slowest
572.0ms
(* (* (* (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)))))
477.0ms
(* (* (* (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)))))
443.0ms
(* -2 (/ (* (log (/ 1 re)) (pow (sqrt 1/2) 2)) (log 10)))
400.0ms
(* (* (* (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)))))
395.0ms
(* -2 (* (pow (/ 1 (pow (log 10) 3)) 1/4) (* (log (/ 1 re)) (sqrt 1/2))))

prune2.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 6.9b

regimes1.1s

Accuracy

51.4% (11.4b remaining)

Error of 18.3b against oracle of 6.9b and baseline of 30.4b

bsearch435.0ms

end1.0ms

sample1.7s

Algorithm
intervals
Results
1.6s8000×body80valid