Details

Time bar (total: 51.0s)

sample964.0ms

Algorithm
intervals
Results
741.0ms212×body10240exit
115.0ms435×body80nan
64.0ms256×body80valid

simplify152.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
151.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

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
14.0ms
(/ (log (hypot re im)) (log base))
0.0ms
(hypot re im)

series229.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
152.0ms
(/ (log (hypot re im)) (log base))
76.0ms
(hypot re im)

simplify1.2s

Counts
46 → 56
Calls
46 calls:
Slowest
452.0ms
(/ (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))) (* (* (log base) (log base)) (log base)))
234.0ms
(* -1 (/ (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))
43.0ms
(/ (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im)))) (* (cbrt (log base)) (cbrt (log base))))
37.0ms
(/ (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im)))) 1)
33.0ms
(/ (log (/ 1 re)) (log (/ 1 base)))

prune483.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.4b
(/ (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (log base))
0.0b
(hypot re im)
0.0b
(hypot re im)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
117×pow1
88×log-pow
68×times-frac
48×sqrt-pow1 pow1/2
47×add-sqr-sqrt
35×*-un-lft-identity add-cube-cbrt
30×pow-prod-up
18×pow-prod-down pow-sqr sqrt-prod
17×associate-/l*
8×add-cbrt-cube swap-sqr add-exp-log
6×pow2 pow-plus associate-*r* associate-*l*
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×hypot-udef
1×cbrt-undiv clear-num rem-square-sqrt frac-2neg sqrt-unprod div-exp prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 178
Calls
4 calls:
Slowest
27.0ms
(/ (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (log base))
8.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0ms
(hypot re im)
0.0ms
(hypot re im)

series377.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(/ (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (log base))
81.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
74.0ms
(hypot re im)
56.0ms
(hypot re im)

simplify3.5s

Counts
225 → 190
Calls
225 calls:
Slowest
587.0ms
(/ (* (* (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (log (* (sqrt (hypot re im)) (sqrt (hypot re im))))) (log (* (sqrt (hypot re im)) (sqrt (hypot re im))))) (* (* (log base) (log base)) (log base)))
237.0ms
(* -1 (/ (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))
157.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
93.0ms
(/ (* 2 (/ 1 2)) (* (cbrt (log base)) (cbrt (log base))))
77.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))

prune2.1s

Pruning

10 alts after pruning (10 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))
0.5b
(* (cbrt (hypot re im)) (cbrt (hypot re im)))

rewrite22.0ms

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
16.0ms
(* (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))

series614.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(cbrt (hypot re im))
152.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
149.0ms
(cbrt (hypot re im))
140.0ms
(cbrt (hypot re im))

simplify1.6s

Counts
65 → 97
Calls
65 calls:
Slowest
270.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
248.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
222.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
205.0ms
(+ (pow im 2/3) (* 1/3 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3))))
74.0ms
(* (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))) (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

3.2b
(expm1 (log1p (cbrt (hypot re im))))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×expm1-log1p expm1-udef
Counts
4 → 54
Calls
4 calls:
Slowest
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(expm1 (log1p (cbrt (hypot re im))))

series703.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
226.0ms
(expm1 (log1p (cbrt (hypot re im))))
163.0ms
(cbrt (hypot re im))
160.0ms
(cbrt (hypot re im))
154.0ms
(cbrt (hypot re im))

simplify1.0s

Counts
22 → 66
Calls
22 calls:
Slowest
241.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
194.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
180.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
162.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
30.0ms
(pow (/ -1 re) -1/3)

prune799.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes358.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample35.5s

Algorithm
intervals
Results
27.7s7766×body10240exit
4.3s15726×body80nan
2.5s8000×body80valid