Details

Time bar (total: 8.4s)

sample68.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
21.0ms239×body80nan

simplify2.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b
(* (log base) (log base))
28.8b
(sqrt (+ (* re re) (* im im)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
25×*-un-lft-identity
23×pow1 add-cube-cbrt
12×log-prod
10×add-exp-log associate-*l* log-pow add-cbrt-cube
9×times-frac
8×associate-*r*
6×distribute-rgt-in distribute-lft-in swap-sqr
4×add-log-exp
3×flip3-+ associate-/r* sqrt-prod flip-+ associate-/l*
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv pow2 rem-sqrt-square frac-2neg pow-plus div-exp clear-num pow-sqr pow-prod-up div-inv
Counts
4 → 110
Calls
4 calls:
43.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
13.0ms
(* (log base) (log base))
30.0ms
(sqrt (+ (* re re) (* im im)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
100.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
168.0ms
(* (log base) (log base))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Counts
122 → 122

prune509.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b
(* (log base) (log base))
0.5b
(* (log base) (log base))
28.8b
(sqrt (+ (* re re) (* im im)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
270×times-frac
163×add-sqr-sqrt
162×*-un-lft-identity
158×add-cube-cbrt
141×sqrt-prod
31×pow1
24×associate-/l*
18×sqrt-div
16×associate-/r/
13×add-exp-log add-cbrt-cube
12×log-prod swap-sqr log-pow
9×flip3-+ flip-+
8×associate-*r* associate-*l* div-inv
6×distribute-rgt-in distribute-lft-in associate-/r*
4×add-log-exp
3×cbrt-undiv div-exp
2×pow2 pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 278
Calls
4 calls:
67.0ms
(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
11.0ms
(* (log base) (log base))
11.0ms
(* (log base) (log base))
15.0ms
(sqrt (+ (* re re) (* im im)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
165.0ms
(* (log base) (log base))
160.0ms
(* (log base) (log base))
47.0ms
(sqrt (+ (* re re) (* im im)))

simplify115.0ms

Counts
290 → 290

prune920.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sqrt (+ (* re re) (* im im))))
28.8b
(sqrt (+ (* re re) (* im im)))
28.8b
(sqrt (+ (* re re) (* im im)))
28.8b
(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 61
Calls
4 calls:
6.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
16.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
39.0ms
(sqrt (+ (* re re) (* im im)))
46.0ms
(sqrt (+ (* re re) (* im im)))
43.0ms
(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Counts
73 → 73

prune482.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b
(* (log base) (log base))
0.5b
(* (log base) (log base))
28.8b
(sqrt (+ (* re re) (* im im)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
36×pow1
28×add-sqr-sqrt
25×*-un-lft-identity
21×add-cube-cbrt
18×log-prod
16×log-pow
14×associate-*l*
12×swap-sqr associate-*r*
10×add-exp-log add-cbrt-cube
9×distribute-rgt-in distribute-lft-in
4×add-log-exp
3×pow-prod-down prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
2×pow2 sqrt-pow1 pow-plus pow1/2 sqrt-div pow-sqr pow-prod-up
1×rem-sqrt-square flip3-+ flip-+
Counts
4 → 115
Calls
4 calls:
21.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms
(* (log base) (log base))
10.0ms
(* (log base) (log base))
8.0ms
(sqrt (+ (* re re) (* im im)))

series490.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
178.0ms
(* (log base) (log base))
170.0ms
(* (log base) (log base))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify147.0ms

Counts
127 → 127

prune431.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.9b

regimes551.0ms

Accuracy

59.7% (10.1b remaining)

Error of 17.4b against oracle of 7.4b and baseline of 32.4b

bsearch125.0ms

Steps
ItersRangePoint
2
2.117882082947689e+145
2.406271033498864e+145
2.1539307017665857e+145
9
-9.154187816574323e+92
-2.7106654859603125e+84
-8.143203660913673e+92

simplify1.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.4s8219×body80nan
878.0ms8000×body80valid