Details

Time bar (total: 9.7s)

sample30.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify2.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.7b
(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
20×pow1
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
4×add-exp-log sqrt-div associate-/r* add-cbrt-cube
3×sqrt-prod
2×log-div flip3-+ div-sub flip-+ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num div-inv
Counts
2 → 63
Calls
2 calls:
27.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
8.0ms
(sqrt (+ (* re re) (* im im)))

series184.0ms

Counts
2 → 6
Calls
2 calls:
144.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify121.0ms

Counts
69 → 69

prune201.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (/ 1 2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
0.6b
(/ (log 10.0) (log (+ (* re re) (* im im))))
31.0b
(log (+ (* re re) (* im im)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
689×times-frac
287×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
126×pow1
123×log-pow
37×div-inv
28×add-exp-log
24×associate-/r*
17×div-exp add-cbrt-cube associate-/l*
9×cbrt-undiv
3×log-prod add-log-exp
2×log-div rec-exp frac-2neg 1-exp clear-num
1×flip3-+ rem-log-exp associate-/r/ flip-+ associate-/l/
Counts
3 → 367
Calls
3 calls:
25.0ms
(/ (/ 1 2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
8.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
6.0ms
(log (+ (* re re) (* im im)))

series339.0ms

Counts
3 → 9
Calls
3 calls:
147.0ms
(/ (/ 1 2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
135.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
57.0ms
(log (+ (* re re) (* im im)))

simplify70.0ms

Counts
376 → 376

prune650.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (/ 1 2)) (/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2)))
0.5b
(/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2))
0.6b
(/ (log 10.0) (log (+ (* re re) (* im im))))
31.0b
(log (+ (* re re) (* im im)))

rewrite400.0ms

Algorithm
rewrite-expression-head
Rules
7029×times-frac
2735×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
2708×sqrt-prod
887×pow1
883×log-pow
254×div-inv
134×associate-/r*
40×associate-/l*
21×add-exp-log
20×add-cbrt-cube
10×cbrt-undiv div-exp
4×add-log-exp
3×log-prod frac-2neg clear-num
2×log-div associate-/l/
1×flip3-+ sqrt-div rem-log-exp associate-/r/ flip-+
Counts
4 → 2353
Calls
4 calls:
84.0ms
(/ (sqrt (/ 1 2)) (/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2)))
17.0ms
(/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2))
8.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
7.0ms
(log (+ (* re re) (* im im)))

series622.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(/ (sqrt (/ 1 2)) (/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2)))
200.0ms
(/ (/ (log 10.0) (log (+ (* re re) (* im im)))) (sqrt 1/2))
141.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
51.0ms
(log (+ (* re re) (* im im)))

simplify494.0ms

Counts
2365 → 2365

prune3.5s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ (sqrt (/ 1 (sqrt 2))) (log 10.0)) (fabs (cbrt 1/2)))
1.0b
(sqrt (/ 1 (sqrt 2)))
1.0b
(sqrt (/ 1 (sqrt 2)))
31.0b
(log (+ (* re re) (* im im)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
226×times-frac
197×sqrt-prod
150×add-sqr-sqrt
120×*-un-lft-identity
114×add-cube-cbrt
104×associate-*l*
38×pow1
26×log-pow
12×sqrt-pow1
10×add-exp-log rem-sqrt-square
9×add-cbrt-cube
7×div-inv unswap-sqr
6×pow-flip
4×pow1/2 add-log-exp
3×log-prod associate-*r*
2×log-div sqrt-div prod-exp cbrt-unprod inv-pow
1×cbrt-undiv flip3-+ div-exp rem-log-exp pow-prod-down associate-*l/ *-commutative flip-+
Counts
4 → 224
Calls
4 calls:
65.0ms
(* (/ (sqrt (/ 1 (sqrt 2))) (log 10.0)) (fabs (cbrt 1/2)))
7.0ms
(sqrt (/ 1 (sqrt 2)))
9.0ms
(sqrt (/ 1 (sqrt 2)))
7.0ms
(log (+ (* re re) (* im im)))

series54.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(* (/ (sqrt (/ 1 (sqrt 2))) (log 10.0)) (fabs (cbrt 1/2)))
0.0ms
(sqrt (/ 1 (sqrt 2)))
0.0ms
(sqrt (/ 1 (sqrt 2)))
54.0ms
(log (+ (* re re) (* im im)))

simplify48.0ms

Counts
230 → 230

prune940.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 5.2b

regimes611.0ms

Accuracy

56.7% (10.9b remaining)

Error of 18.2b against oracle of 7.3b and baseline of 32.5b

bsearch161.0ms

Steps
ItersRangePoint
5
4.1892021600748604e+22
1.264938644655178e+23
1.2464593188755005e+23
8
1.5682154734600212e-268
4.5359150636480397e-265
2.623840975917303e-268
3
-4.736741763343511e-217
-3.5701351023220896e-217
-3.743447547042941e-217
8
-4.27526971693393e+82
-5.849132443619543e+79
-4.219332295965777e+82

simplify2.0ms

end0.0ms

sample1.0s

Algorithm
intervals
Results
827.0ms8000×body80valid