Details

Time bar (total: 12.8s)

sample57.0ms

Algorithm
intervals
Results
26.0ms341×body80valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
1117
2187
done187

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (* x.re y.re) (* x.im y.im))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt sub-neg flip3-- *-un-lft-identity diff-log add-cbrt-cube flip--
Counts
1 → 12
Calls
1 calls:
15.0ms
(- (* x.re y.re) (* x.im y.im))

series59.0ms

Counts
1 → 3
Calls
1 calls:
59.0ms
(- (* x.re y.re) (* x.im y.im))

simplify2.5s

Counts
15 → 15
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
033168
194163
2358149
31291149
44183149
done5001149

prune38.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x.re y.re) (* x.im y.im))
0.3b
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im))))
0.7b
(sqrt (- (* x.re y.re) (* x.im y.im)))
0.7b
(sqrt (- (* x.re y.re) (* x.im y.im)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
9×flip3-- flip--
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 sub-neg pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 99
Calls
4 calls:
13.0ms
(- (* x.re y.re) (* x.im y.im))
95.0ms
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im))))
16.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
14.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (* x.re y.re) (* x.im y.im))
66.0ms
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (sqrt (- (* x.re y.re) (* x.im y.im))))
121.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))
122.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))

simplify865.0ms

Counts
111 → 111
Iterations

Useful iterations: done (860.0ms)

IterNodesCost
01132098
12731515
211381393
done50001358

prune334.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (* (sqrt (sqrt (- (* x.re y.re) (* y.im x.im)))) (sqrt (sqrt (- (* x.re y.re) (* y.im x.im))))))
0.7b
(sqrt (- (* x.re y.re) (* y.im x.im)))
0.7b
(sqrt (- (* x.re y.re) (* y.im x.im)))
0.7b
(sqrt (- (* x.re y.re) (* x.im y.im)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
96×sqrt-div
30×flip3-- flip--
28×frac-times
15×pow1
14×add-sqr-sqrt associate-*r/
13×sqrt-prod
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
8×associate-*l/
7×pow-prod-down
6×sqrt-pow1 pow1/2 associate-*l*
4×add-log-exp
3×rem-sqrt-square prod-exp cbrt-unprod
2×sqrt-unprod unswap-sqr
1×associate-*r* *-commutative
Counts
4 → 97
Calls
4 calls:
144.0ms
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (* (sqrt (sqrt (- (* x.re y.re) (* y.im x.im)))) (sqrt (sqrt (- (* x.re y.re) (* y.im x.im))))))
9.0ms
(sqrt (- (* x.re y.re) (* y.im x.im)))
13.0ms
(sqrt (- (* x.re y.re) (* y.im x.im)))
20.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (sqrt (- (* x.re y.re) (* x.im y.im))) (* (sqrt (sqrt (- (* x.re y.re) (* y.im x.im)))) (sqrt (sqrt (- (* x.re y.re) (* y.im x.im))))))
117.0ms
(sqrt (- (* x.re y.re) (* y.im x.im)))
116.0ms
(sqrt (- (* x.re y.re) (* y.im x.im)))
97.0ms
(sqrt (- (* x.re y.re) (* x.im y.im)))

simplify973.0ms

Counts
109 → 109
Iterations

Useful iterations: done (968.0ms)

IterNodesCost
01663494
14232546
215202251
done50012126

prune498.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

5.0b
(* (* x.re y.re) (* x.im y.im))
13.2b
(/ (* (sqrt (- (* y.re x.re) (* y.im x.im))) (sqrt (- (pow (* x.re y.re) 3) (pow (* y.im x.im) 3)))) (sqrt (+ (* (* x.re y.re) (* x.re y.re)) (+ (* (* x.im y.im) (* x.im y.im)) (* (* x.re y.re) (* x.im y.im))))))
15.5b
(sqrt (- (pow (* x.re y.re) 3) (pow (* y.im x.im) 3)))
23.6b
(sqrt (+ (* (* x.re y.re) (* x.re y.re)) (+ (* (* x.im y.im) (* x.im y.im)) (* (* x.re y.re) (* x.im y.im)))))

rewrite486.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log add-cbrt-cube
18×pow1 sqrt-div sqrt-prod
16×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt
9×prod-exp cbrt-unprod
8×pow-prod-down associate-/l/
7×flip3-- flip--
6×times-frac associate-/r*
4×frac-times add-log-exp difference-of-squares sqr-pow
2×cbrt-undiv rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r/ div-exp associate-*l/ associate-/r/ flip-+
1×difference-cubes sqrt-undiv frac-2neg sqrt-unprod associate-*r* associate-*l* clear-num *-commutative div-inv associate-/l* distribute-lft-out--
Counts
4 → 96
Calls
4 calls:
41.0ms
(* (* x.re y.re) (* x.im y.im))
212.0ms
(/ (* (sqrt (- (* y.re x.re) (* y.im x.im))) (sqrt (- (pow (* x.re y.re) 3) (pow (* y.im x.im) 3)))) (sqrt (+ (* (* x.re y.re) (* x.re y.re)) (+ (* (* x.im y.im) (* x.im y.im)) (* (* x.re y.re) (* x.im y.im))))))
29.0ms
(sqrt (- (pow (* x.re y.re) 3) (pow (* y.im x.im) 3)))
199.0ms
(sqrt (+ (* (* x.re y.re) (* x.re y.re)) (+ (* (* x.im y.im) (* x.im y.im)) (* (* x.re y.re) (* x.im y.im)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* x.re y.re) (* x.im y.im))
294.0ms
(/ (* (sqrt (- (* y.re x.re) (* y.im x.im))) (sqrt (- (pow (* x.re y.re) 3) (pow (* y.im x.im) 3)))) (sqrt (+ (* (* x.re y.re) (* x.re y.re)) (+ (* (* x.im y.im) (* x.im y.im)) (* (* x.re y.re) (* x.im y.im))))))
1.3s
(sqrt (- (pow (* x.re y.re) 3) (pow (* y.im x.im) 3)))
127.0ms
(sqrt (+ (* (* x.re y.re) (* x.re y.re)) (+ (* (* x.im y.im) (* x.im y.im)) (* (* x.re y.re) (* x.im y.im)))))

simplify2.0s

Counts
108 → 108
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02113678
15423002
229192676
done50002672

prune588.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes267.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
197
done97

end0.0ms

sample1.1s

Algorithm
intervals
Results
450.0ms10461×body80valid