Details

Time bar (total: 3.0s)

sample21.0ms

Algorithm
intervals
Results
10.0ms270×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1367
2487
3667
4727
5727

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(- (* x.im y.re) (* x.re y.im))
26.5b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
4.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(- (* x.im y.re) (* x.re y.im))
8.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series150.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ (* y.re y.re) (* y.im y.im))
35.0ms
(- (* x.im y.re) (* x.re y.im))
85.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify36.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0292541
11273493
25002491

prune372.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
17.3b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
3.0ms
(- (* x.im y.re) (* x.re y.im))
11.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* x.im y.re) (* x.re y.im))
113.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify98.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0304910
1990857
23354845
35001845

prune280.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(+ (* y.re y.re) (* y.im y.im))
16.8b
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
20.1b
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
6×times-frac associate-/r*
4×pow1 cbrt-undiv flip3-+ div-exp associate-/r/ flip-+
2×+-commutative frac-2neg prod-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
4 → 68
Calls
4 calls:
4.0ms
(+ (* y.re y.re) (* y.im y.im))
4.0ms
(+ (* y.re y.re) (* y.im y.im))
6.0ms
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
9.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

series143.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* y.re y.re) (* y.im y.im))
27.0ms
(+ (* y.re y.re) (* y.im y.im))
45.0ms
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
45.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0309530
11570442
25001438

prune211.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.9b

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
20.1b
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
29.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
51×times-frac
34×add-cube-cbrt *-un-lft-identity
30×sqrt-prod
24×associate-*r* associate-*l*
21×add-exp-log add-cbrt-cube
9×unswap-sqr
8×pow1 sqrt-div
6×cbrt-undiv div-exp associate-/r/
5×flip3-+ prod-exp cbrt-unprod flip-+
4×add-log-exp
3×associate-/r* div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 130
Calls
4 calls:
22.0ms
(* (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
6.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series164.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
45.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify63.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05771545
125911391
250011322

prune364.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.7b

regimes100.0ms

Accuracy

0% (1.2b remaining)

Error of 22.9b against oracle of 21.7b and baseline of 22.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01823
11823

end0.0ms

sample530.0ms

Algorithm
intervals
Results
306.0ms8455×body80valid