Details

Time bar (total: 49.6s)

sample46.0ms

Algorithm
intervals
Results
34.0ms256×body80valid

simplify14.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite63.0ms

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
53.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
7.0ms
(sqrt (+ (* re re) (* im im)))

series256.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
182.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
75.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.8s

Counts
72 → 71
Calls
72 calls:
Slowest
482.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
334.0ms
(sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))
299.0ms
(/ (log (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (log 10))
244.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
219.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune829.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
194×sqrt-pow1
175×pow1
136×log-pow
100×times-frac
98×pow1/2
81×add-sqr-sqrt
72×sqrt-prod
54×pow-prod-up
52×sqrt-div
49×*-un-lft-identity add-cube-cbrt
30×pow-prod-down pow-sqr
25×associate-/l*
15×swap-sqr
14×flip3-+ flip-+
9×associate-*r* associate-*l* unswap-sqr
8×frac-times log-div add-cbrt-cube div-sub add-exp-log
6×pow2 pow-plus
4×associate-/r* associate-*l/ associate-*r/ insert-posit16 add-log-exp
2×rem-sqrt-square
1×cbrt-undiv clear-num rem-square-sqrt frac-2neg sqrt-unprod div-exp prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 266
Calls
4 calls:
Slowest
162.0ms
(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (log 10))
39.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
18.0ms
(sqrt (+ (* re re) (* im im)))
12.0ms
(sqrt (+ (* re re) (* im im)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
201.0ms
(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (log 10))
55.0ms
(sqrt (+ (* re re) (* im im)))
49.0ms
(sqrt (+ (* re re) (* im im)))
47.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))

simplify15.8s

Counts
378 → 278
Calls
378 calls:
Slowest
589.0ms
(/ (* (* (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))))) (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))))) (* (* (log 10) (log 10)) (log 10)))
416.0ms
(* (sqrt (sqrt (- (* re re) (* im im)))) (sqrt (sqrt (+ (* (* re re) (* re re)) (- (* (* im im) (* im im)) (* (* re re) (* im im)))))))
362.0ms
(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))))) (log 10))
359.0ms
(* (sqrt (sqrt (+ (* (* re re) (* re re)) (- (* (* im im) (* im im)) (* (* re re) (* im im)))))) (sqrt (sqrt (- (* re re) (* im im)))))
352.0ms
(/ (log (* (sqrt (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (sqrt (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))))) (log 10))

prune3.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.0b

localize25.0ms

Local error

Found 3 expressions with local error:

30.5b
(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))))

rewrite74.0ms

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
40.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
20.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
11.0ms
(log (+ (* re re) (* im im)))

series519.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
268.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
172.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
79.0ms
(log (+ (* re re) (* im im)))

simplify7.6s

Counts
170 → 165
Calls
170 calls:
Slowest
729.0ms
(* (* (* (/ 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)))))
414.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
338.0ms
(* (/ (* (* 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)))))
336.0ms
(/ (log (+ (pow (* re re) 3) (pow (* im im) 3))) (sqrt (log 10)))
280.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize34.0ms

Local error

Found 3 expressions with local error:

30.5b
(log (+ (* re re) (* im im)))
0.3b
(* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))
0.2b
(* (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
44×times-frac
43×add-sqr-sqrt
35×*-un-lft-identity add-cube-cbrt
29×add-cbrt-cube associate-*r*
26×associate-*l*
25×sqrt-prod
22×prod-exp
18×pow1
12×cbrt-unprod
11×div-exp
9×log-prod
8×log-pow
6×cbrt-undiv
4×pow-prod-down associate-*l/
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp insert-posit16 add-log-exp unswap-sqr
2×log-div *-commutative div-inv
1×frac-times flip3-+ rem-log-exp associate-*r/ un-div-inv flip-+
Counts
3 → 127
Calls
3 calls:
Slowest
42.0ms
(* (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10))))
23.0ms
(* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))
10.0ms
(log (+ (* re re) (* im im)))

series655.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
343.0ms
(* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))
240.0ms
(* (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10))))
72.0ms
(log (+ (* re re) (* im im)))

simplify10.5s

Counts
111 → 136
Calls
111 calls:
Slowest
532.0ms
(+ (+ (- (log 1/2) (log (sqrt (log 10)))) (log (log (+ (* re re) (* im im))))) (- (log 1) (log (sqrt (log 10)))))
482.0ms
(+ (+ (- (log 1/2) (log (sqrt (log 10)))) (log (log (+ (* re re) (* im im))))) (log (/ 1 (sqrt (log 10)))))
466.0ms
(+ (+ (log (/ 1/2 (sqrt (log 10)))) (log (log (+ (* re re) (* im im))))) (- (log 1) (log (sqrt (log 10)))))
460.0ms
(+ (+ (log (/ 1/2 (sqrt (log 10)))) (log (log (+ (* re re) (* im im))))) (- 0 (log (sqrt (log 10)))))
447.0ms
(+ (log (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))) (- (log 1) (log (sqrt (log 10)))))

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

regimes795.0ms

Accuracy

54% (10.9b remaining)

Error of 18.4b against oracle of 7.4b and baseline of 31.2b

bsearch309.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.2s8000×body80valid