Details

Time bar (total: 14.0s)

sample37.0ms

Algorithm
intervals
Results
16.0ms272×body80valid

simplify42.0ms

Counts
1 → 1
Iterations
IterNodes
done72
572
466
348
236
119
011

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x.im y.re) (* x.re y.im))
23.2b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
2 → 44
Calls
2 calls:
10.0ms
(- (* x.im y.re) (* x.re y.im))
19.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series168.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(- (* x.im y.re) (* x.re y.im))
113.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts
50 → 50
Iterations
IterNodes
done5000
21073
1258
089

prune334.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.8b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×flip3-+ add-cbrt-cube add-exp-log flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×flip3-- flip--
Counts
4 → 266
Calls
4 calls:
37.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
20.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
174.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
59.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
46.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts
278 → 278
Iterations
IterNodes
done5000
23205
1764
0307

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
14.8b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
100×add-sqr-sqrt
98×*-un-lft-identity add-cube-cbrt
54×sqrt-prod
27×associate-/r*
17×add-exp-log
11×add-cbrt-cube associate-/r/
9×associate-/l*
8×div-exp
7×pow1
6×sqrt-div div-inv
5×flip3-- flip--
4×cbrt-undiv add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp associate-/l/
1×pow-flip inv-pow
Counts
4 → 193
Calls
4 calls:
37.0ms
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
18.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
102.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
60.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts
205 → 205
Iterations
IterNodes
done5000
23489
1642
0243

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.3b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* x.im y.re) (* x.re y.im))
0.7b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
23.1b
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×*-un-lft-identity times-frac
19×add-cube-cbrt
16×add-exp-log
15×associate-*r*
10×add-cbrt-cube
6×pow1
5×add-log-exp
4×div-exp prod-exp associate-/r/
3×associate-/r* flip3-- associate-*l* flip-- associate-/l* unswap-sqr
2×frac-times cbrt-undiv rec-exp flip3-+ 1-exp associate-*l/ cbrt-unprod flip-+ div-inv
1×clear-num sub-neg frac-2neg diff-log pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
3 → 87
Calls
3 calls:
6.0ms
(- (* x.im y.re) (* x.re y.im))
19.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
67.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series218.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(- (* x.im y.re) (* x.re y.im))
59.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
113.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify2.6s

Counts
96 → 96
Iterations
IterNodes
done5000
22683
1365
0128

prune474.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.3b

regimes321.0ms

Accuracy

0% (2.8b remaining)

Error of 26.4b against oracle of 23.6b and baseline of 26.4b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done20
120
015

end0.0ms

sample1.4s

Algorithm
intervals
Results
900.0ms8438×body80valid