Details

Time bar (total: 1.9m)

sample1.1s

Algorithm
intervals
Results
798.0ms270×body10240exit
166.0ms474×body80nan
58.0ms256×body80valid

simplify109.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
109.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ (log (hypot re im)) (log base))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
16×times-frac
11×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
10×log-pow
4×associate-/r* associate-/l*
3×add-cbrt-cube add-exp-log
1×expm1-log1p-u cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 39
Calls
1 calls:
Slowest
7.0ms
(/ (log (hypot re im)) (log base))

series118.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
118.0ms
(/ (log (hypot re im)) (log base))

simplify1.2s

Counts
43 → 42
Calls
43 calls:
Slowest
511.0ms
(/ (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))) (* (* (log base) (log base)) (log base)))
229.0ms
(* -1 (/ (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))
60.0ms
(/ (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im)))) (* (cbrt (log base)) (cbrt (log base))))
32.0ms
(/ (log (/ 1 re)) (log (/ 1 base)))
28.0ms
(/ (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im)))) 1)

prune542.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (log base) (log (hypot re im)))
0.2b
(/ 1 (/ (log base) (log (hypot re im))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
69×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
45×pow1
42×log-pow
24×associate-/r*
15×add-exp-log
9×add-cbrt-cube
8×div-exp
7×associate-/l*
6×div-inv
4×cbrt-undiv
2×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp insert-posit16 log1p-expm1-u add-log-exp
1×associate-/r/ pow-flip inv-pow
Counts
2 → 146
Calls
2 calls:
Slowest
11.0ms
(/ 1 (/ (log base) (log (hypot re im))))
6.0ms
(/ (log base) (log (hypot re im)))

series414.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
216.0ms
(/ (log base) (log (hypot re im)))
197.0ms
(/ 1 (/ (log base) (log (hypot re im))))

simplify9.2s

Counts
196 → 152
Calls
196 calls:
Slowest
754.0ms
(* -1 (/ (- (log -1) (log (/ -1 base))) (log (/ -1 re))))
532.0ms
(/ (* (* 1 1) 1) (* (* (/ (log base) (log (hypot re im))) (/ (log base) (log (hypot re im)))) (/ (log base) (log (hypot re im)))))
490.0ms
(/ (* (* (log base) (log base)) (log base)) (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))))
342.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (log base)) (cbrt (log base))) (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im))))))
303.0ms
(/ (sqrt 1) (/ (* (cbrt (log base)) (cbrt (log base))) (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im))))))

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (/ 1 (log base)) (/ 1 (log (hypot re im))))
0.3b
(/ 1 (log (hypot re im)))
0.3b
(/ 1 (log base))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
688×times-frac
293×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
115×pow1
110×log-pow
51×add-exp-log
37×div-inv
36×div-exp
24×associate-/r*
22×associate-/l*
19×add-cbrt-cube
10×cbrt-undiv rec-exp 1-exp
3×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×pow-flip inv-pow
1×associate-/r/ associate-/l/
Counts
3 → 399
Calls
3 calls:
Slowest
10.0ms
(/ (/ 1 (log base)) (/ 1 (log (hypot re im))))
4.0ms
(/ 1 (log base))
4.0ms
(/ 1 (log (hypot re im)))

series625.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
286.0ms
(/ 1 (log base))
198.0ms
(/ (/ 1 (log base)) (/ 1 (log (hypot re im))))
140.0ms
(/ 1 (log (hypot re im)))

simplify42.8s

Counts
640 → 408
Calls
640 calls:
Slowest
1.1s
(/ (* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base))) (* (* (/ 1 (log (hypot re im))) (/ 1 (log (hypot re im)))) (/ 1 (log (hypot re im)))))
601.0ms
(/ (/ 1 (* (cbrt (log base)) (cbrt (log base)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im))))))
458.0ms
(/ (/ (* (* 1 1) 1) (* (* (log base) (log base)) (log base))) (/ (* (* 1 1) 1) (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im)))))
450.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (log base)) (cbrt (log base)))) (/ (sqrt 1) (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im))))))
443.0ms
(/ (sqrt (/ 1 (log base))) (/ (cbrt 1) (log (hypot re im))))

prune4.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b
(exp (/ (log base) (log (hypot re im))))
0.4b
(log (exp (/ (log base) (log (hypot re im)))))
0.4b
(/ (log base) (log (hypot re im)))
0.2b
(/ 1 (log (exp (/ (log base) (log (hypot re im))))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
187×times-frac
168×log-pow
120×exp-prod
99×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
68×pow1
29×associate-/r*
14×div-inv
10×add-exp-log
8×add-cbrt-cube
7×associate-/l*
6×exp-to-pow
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod div-exp
2×cbrt-undiv clear-num frac-2neg
1×rec-exp 1-exp rem-log-exp pow-flip inv-pow rem-exp-log
Counts
4 → 229
Calls
4 calls:
Slowest
18.0ms
(/ 1 (log (exp (/ (log base) (log (hypot re im))))))
9.0ms
(exp (/ (log base) (log (hypot re im))))
6.0ms
(log (exp (/ (log base) (log (hypot re im)))))
6.0ms
(/ (log base) (log (hypot re im)))

series894.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
301.0ms
(exp (/ (log base) (log (hypot re im))))
217.0ms
(/ (log base) (log (hypot re im)))
193.0ms
(log (exp (/ (log base) (log (hypot re im)))))
183.0ms
(/ 1 (log (exp (/ (log base) (log (hypot re im))))))

simplify13.0s

Counts
279 → 241
Calls
279 calls:
Slowest
884.0ms
(* -1 (/ (- (log -1) (log (/ -1 base))) (log (/ -1 re))))
839.0ms
(* -1 (/ (- (log -1) (log (/ -1 base))) (log (/ -1 re))))
471.0ms
(/ (* (* (log base) (log base)) (log base)) (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))))
359.0ms
(exp (* -1 (/ (- (log -1) (log (/ -1 base))) (log (/ -1 re)))))
326.0ms
(/ (cbrt 1) (log (exp (/ (* (cbrt (log base)) (cbrt (log base))) (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im))))))))

prune3.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes303.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch1.0ms

end0.0ms

sample35.9s

Algorithm
intervals
Results
28.1s8107×body10240exit
4.7s16079×body80nan
2.3s8000×body80valid