Details

Time bar (total: 58.5s)

sample1.1s

Algorithm
intervals
Results
863.0ms270×body10240exit
122.0ms506×body80nan
60.0ms256×body80valid

simplify143.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
143.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (log (hypot re im)) (log base))
0.0b
(hypot re im)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
16×times-frac
12×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
10×log-pow
4×associate-/r* add-cbrt-cube add-exp-log associate-/l*
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv hypot-udef clear-num frac-2neg div-exp div-inv
Counts
2 → 50
Calls
2 calls:
Slowest
15.0ms
(/ (log (hypot re im)) (log base))
0.0ms
(hypot re im)

series256.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
169.0ms
(/ (log (hypot re im)) (log base))
87.0ms
(hypot re im)

simplify1.1s

Counts
46 → 56
Calls
46 calls:
Slowest
448.0ms
(/ (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))) (* (* (log base) (log base)) (log base)))
216.0ms
(* -1 (/ (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))
46.0ms
(/ (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im)))) (* (cbrt (log base)) (cbrt (log base))))
38.0ms
(/ (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im)))) 1)
30.0ms
(/ (log (/ 1 re)) (log (/ 1 base)))

prune574.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.6b
(* (cbrt (hypot re im)) (cbrt (hypot re im)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
8.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))

series595.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(cbrt (hypot re im))
154.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
147.0ms
(cbrt (hypot re im))
137.0ms
(cbrt (hypot re im))

simplify1.4s

Counts
65 → 97
Calls
65 calls:
Slowest
214.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
201.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
197.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
193.0ms
(+ (pow im 2/3) (* 1/3 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3))))
105.0ms
(* (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))) (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (log base) (log (hypot re im)))
0.2b
(/ 1 (/ (log base) (log (hypot re im))))
0.0b
(hypot re im)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
70×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
46×pow1
42×log-pow
24×associate-/r*
16×add-exp-log
10×add-cbrt-cube
8×div-exp
7×associate-/l*
6×div-inv
4×cbrt-undiv
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rec-exp clear-num frac-2neg 1-exp
1×hypot-udef associate-/r/ pow-flip inv-pow
Counts
3 → 157
Calls
3 calls:
Slowest
19.0ms
(/ (log base) (log (hypot re im)))
14.0ms
(/ 1 (/ (log base) (log (hypot re im))))
0.0ms
(hypot re im)

series397.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
185.0ms
(/ (log base) (log (hypot re im)))
156.0ms
(/ 1 (/ (log base) (log (hypot re im))))
56.0ms
(hypot re im)

simplify9.2s

Counts
199 → 166
Calls
199 calls:
Slowest
808.0ms
(* -1 (/ (- (log -1) (log (/ -1 base))) (log (/ -1 re))))
515.0ms
(/ (* (* 1 1) 1) (* (* (/ (log base) (log (hypot re im))) (/ (log base) (log (hypot re im)))) (/ (log base) (log (hypot re im)))))
499.0ms
(/ (* (* (log base) (log base)) (log base)) (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))))
325.0ms
(/ (sqrt 1) (/ (* (cbrt (log base)) (cbrt (log base))) (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im))))))
287.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (log base)) (cbrt (log base))) (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im))))))

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (log base)) (log (hypot re im)))
0.3b
(/ 1 (log base))
0.0b
(hypot re im)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×times-frac
24×*-un-lft-identity
23×add-cube-cbrt
16×associate-*l* add-exp-log
14×pow1
10×add-cbrt-cube
8×log-pow
6×log-prod
4×associate-/r* div-exp associate-*r* prod-exp
3×distribute-rgt-in expm1-log1p-u distribute-lft-in insert-posit16 log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv rec-exp 1-exp cbrt-unprod div-inv
1×hypot-udef clear-num frac-2neg pow-prod-down associate-*l/ *-commutative pow-flip inv-pow
Counts
3 → 97
Calls
3 calls:
Slowest
22.0ms
(* (/ 1 (log base)) (log (hypot re im)))
5.0ms
(/ 1 (log base))
0.0ms
(hypot re im)

series434.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
203.0ms
(/ 1 (log base))
176.0ms
(* (/ 1 (log base)) (log (hypot re im)))
56.0ms
(hypot re im)

simplify3.0s

Counts
81 → 106
Calls
81 calls:
Slowest
717.0ms
(* (/ (* (* 1 1) 1) (* (* (log base) (log base)) (log base))) (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))))
379.0ms
(* (* (* (/ 1 (log base)) (/ 1 (log base))) (/ 1 (log base))) (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))))
204.0ms
(* -1 (/ (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))
128.0ms
(/ (* (* 1 1) 1) (* (* (log base) (log base)) (log base)))
99.0ms
(+ (- 0 (log (log base))) (log (log (hypot re im))))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes246.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample35.4s

Algorithm
intervals
Results
26.7s8049×body10240exit
5.2s15802×body80nan
2.5s8000×body80valid