Details

Time bar (total: 27.8s)

sample33.0ms

Algorithm
intervals
Results
23.0ms256×body80valid

simplify22.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
22.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 1 expressions with local error:

0.6b
(/ (log (hypot re im)) (log 10))

rewrite7.0ms

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
6.0ms
(/ (log (hypot re im)) (log 10))

series186.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
186.0ms
(/ (log (hypot re im)) (log 10))

simplify1.1s

Counts
43 → 42
Calls
43 calls:
Slowest
435.0ms
(/ (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))) (* (* (log 10) (log 10)) (log 10)))
107.0ms
(* -1 (/ (log (/ -1 re)) (log 10)))
95.0ms
(* -1 (/ (log (/ 1 re)) (log 10)))
44.0ms
(/ (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im)))) (* (cbrt (log 10)) (cbrt (log 10))))
29.0ms
(/ (* (cbrt (log (hypot re im))) (cbrt (log (hypot re im)))) 1)

prune519.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 2 expressions with local error:

0.5b
(/ (log (hypot re im)) (sqrt (log 10)))
0.3b
(* (/ 1 (sqrt (log 10))) (/ (log (hypot re im)) (sqrt (log 10))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
99×times-frac
96×add-sqr-sqrt
59×sqrt-prod
56×*-un-lft-identity
50×add-cube-cbrt
32×associate-*r*
31×pow1
27×log-pow
26×add-exp-log
25×associate-*l*
16×add-cbrt-cube
15×unswap-sqr
9×div-exp
8×prod-exp
7×associate-/r*
5×cbrt-undiv
4×cbrt-unprod associate-/l*
3×div-inv
2×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
2 → 153
Calls
2 calls:
Slowest
40.0ms
(* (/ 1 (sqrt (log 10))) (/ (log (hypot re im)) (sqrt (log 10))))
14.0ms
(/ (log (hypot re im)) (sqrt (log 10)))

series501.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
313.0ms
(/ (log (hypot re im)) (sqrt (log 10)))
188.0ms
(* (/ 1 (sqrt (log 10))) (/ (log (hypot re im)) (sqrt (log 10))))

simplify7.4s

Counts
175 → 159
Calls
175 calls:
Slowest
458.0ms
(* (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))) (* (* (/ (log (hypot re im)) (sqrt (log 10))) (/ (log (hypot re im)) (sqrt (log 10)))) (/ (log (hypot re im)) (sqrt (log 10)))))
395.0ms
(/ (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
252.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))) (/ (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))))
227.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))) (* (* (/ (log (hypot re im)) (sqrt (log 10))) (/ (log (hypot re im)) (sqrt (log 10)))) (/ (log (hypot re im)) (sqrt (log 10)))))
198.0ms
(* (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))) (/ (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 2 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
76×add-exp-log
46×times-frac
45×add-sqr-sqrt
40×prod-exp
35×*-un-lft-identity
33×add-cube-cbrt
29×associate-*r*
28×add-cbrt-cube
26×associate-*l* sqrt-prod
20×div-exp
16×pow1
12×cbrt-unprod
10×rec-exp 1-exp
7×log-pow
6×cbrt-undiv log-prod
5×unswap-sqr
4×pow-prod-down associate-*l/
3×distribute-rgt-in distribute-lft-in
2×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u div-inv add-log-exp
1×frac-times associate-*r/ un-div-inv
Counts
2 → 128
Calls
2 calls:
Slowest
39.0ms
(* (* (/ 1 (sqrt (log 10))) (log (hypot re im))) (/ 1 (sqrt (log 10))))
21.0ms
(* (/ 1 (sqrt (log 10))) (log (hypot re im)))

series524.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
316.0ms
(* (/ 1 (sqrt (log 10))) (log (hypot re im)))
207.0ms
(* (* (/ 1 (sqrt (log 10))) (log (hypot re im))) (/ 1 (sqrt (log 10))))

simplify8.4s

Counts
116 → 134
Calls
116 calls:
Slowest
658.0ms
(* (* (* (* (/ 1 (sqrt (log 10))) (log (hypot re im))) (* (/ 1 (sqrt (log 10))) (log (hypot re im)))) (* (/ 1 (sqrt (log 10))) (log (hypot re im)))) (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))))
482.0ms
(* (* (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))) (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im)))) (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))))
443.0ms
(* (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))) (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))))
380.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))) (* (* (log (hypot re im)) (log (hypot re im))) (log (hypot re im))))
228.0ms
(* (* (* (* (/ 1 (sqrt (log 10))) (log (hypot re im))) (* (/ 1 (sqrt (log 10))) (log (hypot re im)))) (* (/ 1 (sqrt (log 10))) (log (hypot re im)))) (/ (* (* 1 1) 1) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

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)))

rewrite21.0ms

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
15.0ms
(* (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))

series735.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
203.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
192.0ms
(cbrt (hypot re im))
177.0ms
(cbrt (hypot re im))
164.0ms
(cbrt (hypot re im))

simplify1.4s

Counts
65 → 97
Calls
65 calls:
Slowest
216.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
203.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
200.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
152.0ms
(+ (pow im 2/3) (* 1/3 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3))))
114.0ms
(* (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))) (* (cbrt (cbrt (hypot re im))) (cbrt (cbrt (hypot re im)))))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes149.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.6s8000×body80valid