Details

Time bar (total: 43.1s)

sample59.0ms

Algorithm
intervals
Results
43.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize30.0ms

Local error

Found 2 expressions with local error:

27.7b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

rewrite60.0ms

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
43.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
14.0ms
(sqrt (+ (* re re) (* im im)))

series231.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
165.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
66.0ms
(sqrt (+ (* re re) (* im im)))

simplify4.5s

Counts
101 → 71
Calls
101 calls:
Slowest
505.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
313.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
308.0ms
(/ (log (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (log 10))
303.0ms
(/ (log (sqrt (+ (* (* re re) (* re re)) (- (* (* im im) (* im im)) (* (* re re) (* im im)))))) (log 10))
296.0ms
(sqrt (+ (* (* re re) (* re re)) (- (* (* im im) (* im im)) (* (* re re) (* im im)))))

prune743.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize32.0ms

Local error

Found 3 expressions with local error:

28.8b
(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))))

rewrite90.0ms

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
39.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
36.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
10.0ms
(log (+ (* re re) (* im im)))

series481.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
248.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
170.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
63.0ms
(log (+ (* re re) (* im im)))

simplify16.1s

Counts
209 → 165
Calls
209 calls:
Slowest
645.0ms
(* (* (* (/ 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)))))
445.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
393.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im))))) (* (cbrt (sqrt (log 10))) (cbrt (sqrt (log 10))))))
341.0ms
(* (/ (* (* 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)))))
340.0ms
(log (+ (* (* re re) (* re re)) (- (* (* im im) (* im im)) (* (* re re) (* im im)))))

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize65.0ms

Local error

Found 4 expressions with local error:

28.8b
(log (+ (* re re) (* im im)))
1.0b
(sqrt (sqrt (log 10)))
1.0b
(sqrt (sqrt (log 10)))
1.0b
(* (cbrt 1/2) (cbrt 1/2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
24×sqrt-prod
18×pow1
17×*-un-lft-identity add-cube-cbrt
16×cbrt-prod
8×sqrt-pow1
7×add-exp-log
6×pow1/3 swap-sqr associate-*r* associate-*l*
4×rem-sqrt-square add-cbrt-cube pow1/2 insert-posit16 add-log-exp unswap-sqr
3×log-prod log-pow
2×log-div pow-prod-down pow-sqr pow-prod-up
1×pow2 flip3-+ pow-plus rem-log-exp prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 98
Calls
4 calls:
Slowest
8.0ms
(* (cbrt 1/2) (cbrt 1/2))
6.0ms
(log (+ (* re re) (* im im)))
2.0ms
(sqrt (sqrt (log 10)))
2.0ms
(sqrt (sqrt (log 10)))

series65.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
65.0ms
(log (+ (* re re) (* im im)))
0.0ms
(sqrt (sqrt (log 10)))
0.0ms
(* (cbrt 1/2) (cbrt 1/2))
0.0ms
(sqrt (sqrt (log 10)))

simplify2.5s

Counts
124 → 104
Calls
124 calls:
Slowest
317.0ms
(log (+ (* (* re re) (* re re)) (- (* (* im im) (* im im)) (* (* re re) (* im im)))))
299.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))
215.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))
132.0ms
(* (/ (cbrt 1/2) (sqrt (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
131.0ms
(* (/ (cbrt 1/2) (sqrt (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.2b

localize26.0ms

Local error

Found 3 expressions with local error:

28.8b
(log (+ (* re re) (* im im)))
0.4b
(/ (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (sqrt (log 10)))
0.3b
(* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
30×times-frac
25×*-un-lft-identity associate-*l* add-cube-cbrt
21×sqrt-prod
18×add-exp-log
17×add-cbrt-cube
12×pow1
9×log-prod
7×associate-/r* log-pow
5×cbrt-undiv div-exp
4×associate-*r* prod-exp cbrt-unprod
3×distribute-rgt-in distribute-lft-in insert-posit16 add-log-exp unswap-sqr
2×log-div associate-*l/ div-inv
1×clear-num frac-2neg flip3-+ rem-log-exp pow-prod-down *-commutative flip-+ associate-/l* associate-/l/
Counts
3 → 101
Calls
3 calls:
Slowest
38.0ms
(/ (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (sqrt (log 10)))
21.0ms
(* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))
5.0ms
(log (+ (* re re) (* im im)))

series596.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
341.0ms
(* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))
182.0ms
(/ (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (sqrt (log 10)))
72.0ms
(log (+ (* re re) (* im im)))

simplify10.3s

Counts
130 → 110
Calls
130 calls:
Slowest
832.0ms
(* (* (/ (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (sqrt (log 10))) (/ (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (sqrt (log 10)))) (/ (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (sqrt (log 10))))
500.0ms
(log (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))))
344.0ms
(/ (* (* (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))) (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
330.0ms
(/ (* (/ (* (* 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))))
325.0ms
(* (* (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))) (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im))))) (* (/ 1/2 (sqrt (log 10))) (log (+ (* re re) (* im im)))))

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.2b

regimes815.0ms

Accuracy

57% (10.2b remaining)

Error of 17.3b against oracle of 7.1b and baseline of 30.9b

bsearch249.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.2s8000×body80valid