Details

Time bar (total: 30.8s)

sample44.0ms

Algorithm
intervals
Results
34.0ms256×body80valid

simplify10.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize18.0ms

Local error

Found 3 expressions with local error:

30.5b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite29.0ms

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
14.0ms
(sqrt (+ (* re re) (* im im)))
11.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
3.0ms
(+ (* re re) (* im im))

series316.0ms

Calls
3 calls:
Slowest
200.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
64.0ms
(sqrt (+ (* re re) (* im im)))
52.0ms
(+ (* re re) (* im im))

simplify1.8s

Calls
55 calls:
Slowest
237.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
219.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
180.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
126.0ms
(/ (log (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (log 10))
117.0ms
(* -1 (/ (log (/ 1 re)) (log 10)))

prune865.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.8b

localize10.0ms

Local error

Found 4 expressions with local error:

30.5b
(sqrt (+ (* re re) (* im im)))
0.5b
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10)))
0.3b
(* (/ 1 (sqrt (log 10))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10))))
0.0b
(+ (* re re) (* im im))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
43×add-sqr-sqrt
42×*-un-lft-identity add-cube-cbrt
36×sqrt-prod
34×associate-*r*
26×log-pow
19×pow1
16×add-exp-log
14×pow1/2
11×add-cbrt-cube
6×associate-/r* add-log-exp
5×associate-/l*
4×sqrt-div associate-*l* prod-exp insert-posit16
3×flip3-+ div-exp flip-+ div-inv
2×cbrt-undiv log-div rec-exp div-sub cbrt-unprod
1×frac-times +-commutative rem-sqrt-square clear-num sum-log frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Calls
4 calls:
Slowest
13.0ms
(* (/ 1 (sqrt (log 10))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10))))
11.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10)))
3.0ms
(+ (* re re) (* im im))
2.0ms
(sqrt (+ (* re re) (* im im)))

series509.0ms

Calls
4 calls:
Slowest
265.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10)))
161.0ms
(* (/ 1 (sqrt (log 10))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10))))
41.0ms
(sqrt (+ (* re re) (* im im)))
41.0ms
(+ (* re re) (* im im))

simplify4.9s

Calls
138 calls:
Slowest
545.0ms
(* (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))) (* (* (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10)))))
259.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (sqrt (log 10)))
252.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
223.0ms
(* (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))) (/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))))
213.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.6b

localize5.0ms

Local error

Found 4 expressions with local error:

30.5b
(sqrt (+ (* re re) (* im im)))
0.3b
(* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im)))))
0.3b
(* (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im))))) (/ 1 (sqrt (log 10))))
0.0b
(+ (* re re) (* im im))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
13×add-sqr-sqrt
12×pow1 log-prod *-un-lft-identity prod-exp add-cube-cbrt
11×add-cbrt-cube
9×associate-*r* sqrt-prod
6×distribute-rgt-in rec-exp distribute-lft-in add-log-exp
5×associate-*l*
4×pow-prod-down associate-*l/ cbrt-unprod insert-posit16
2×flip3-+ pow1/2 sqrt-div log-pow *-commutative flip-+ div-inv
1×frac-times +-commutative rem-sqrt-square sum-log associate-*r/ un-div-inv
Calls
4 calls:
Slowest
27.0ms
(* (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im))))) (/ 1 (sqrt (log 10))))
8.0ms
(* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im)))))
5.0ms
(+ (* re re) (* im im))
2.0ms
(sqrt (+ (* re re) (* im im)))

series634.0ms

Calls
4 calls:
Slowest
335.0ms
(* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im)))))
197.0ms
(* (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im))))) (/ 1 (sqrt (log 10))))
70.0ms
(sqrt (+ (* re re) (* im im)))
31.0ms
(+ (* re re) (* im im))

simplify4.9s

Calls
63 calls:
Slowest
569.0ms
(* (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))) (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))))
554.0ms
(* (* (* (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im))))) (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im)))))) (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im)))))) (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))))
514.0ms
(* (* (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))) (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im)))))) (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))))
224.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
180.0ms
(+ (log (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im)))))) (- (log (sqrt (log 10)))))

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.6b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
21×pow1
20×add-cbrt-cube
19×associate-*r*
17×sqrt-prod
16×add-sqr-sqrt prod-exp
15×*-un-lft-identity add-cube-cbrt
13×associate-*l/
12×log-prod sqrt-div
10×pow-prod-down cbrt-unprod
6×distribute-rgt-in frac-times distribute-lft-in associate-*l*
4×associate-*r/ insert-posit16 add-log-exp
3×rec-exp *-commutative div-inv
2×pow1/2 log-pow
1×rem-sqrt-square flip3-+ flip-+
Calls
4 calls:
Slowest
78.0ms
(* (* (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im))))) (sqrt (/ 1 (sqrt (log 10))))) (sqrt (/ 1 (sqrt (log 10)))))
29.0ms
(* (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im))))) (sqrt (/ 1 (sqrt (log 10)))))
8.0ms
(* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im)))))
2.0ms
(sqrt (+ (* re re) (* im im)))

series1.2s

Calls
4 calls:
Slowest
558.0ms
(* (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im))))) (sqrt (/ 1 (sqrt (log 10)))))
293.0ms
(* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im)))))
234.0ms
(* (* (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im))))) (sqrt (/ 1 (sqrt (log 10))))) (sqrt (/ 1 (sqrt (log 10)))))
65.0ms
(sqrt (+ (* re re) (* im im)))

simplify7.5s

Calls
89 calls:
Slowest
551.0ms
(* -1 (* (log (/ -1 re)) (pow (/ 1 (pow (log 10) 3)) 1/4)))
455.0ms
(* (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))) (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))))
340.0ms
(* (* (* (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))) (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im)))))) (* (* (sqrt (/ 1 (sqrt (log 10)))) (sqrt (/ 1 (sqrt (log 10))))) (sqrt (/ 1 (sqrt (log 10)))))) (* (* (sqrt (/ 1 (sqrt (log 10)))) (sqrt (/ 1 (sqrt (log 10))))) (sqrt (/ 1 (sqrt (log 10))))))
313.0ms
(* (* (* (* (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im))))) (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im)))))) (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im)))))) (* (* (sqrt (/ 1 (sqrt (log 10)))) (sqrt (/ 1 (sqrt (log 10))))) (sqrt (/ 1 (sqrt (log 10)))))) (* (* (sqrt (/ 1 (sqrt (log 10)))) (sqrt (/ 1 (sqrt (log 10))))) (sqrt (/ 1 (sqrt (log 10))))))
292.0ms
(+ (log (* (* (/ 1 (sqrt (log 10))) (log (sqrt (+ (* re re) (* im im))))) (sqrt (/ 1 (sqrt (log 10)))))) (log (sqrt (/ 1 (sqrt (log 10))))))

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.6b

regimes1.3s

Accuracy

54.4% (10.9b remaining)

Error of 18.4b against oracle of 7.5b and baseline of 31.4b

bsearch316.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.2s8000×body80valid