Details

Time bar (total: 3.5s)

sample38.0ms

Algorithm
intervals
Results
27.0ms268×body80valid

simplify11.0ms

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: 26.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.2b
(- (* x.im y.re) (* x.re y.im))
26.2b
(/ (- (* 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:
2.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(- (* x.im y.re) (* x.re y.im))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series147.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* y.re y.re) (* y.im y.im))
35.0ms
(- (* x.im y.re) (* x.re y.im))
83.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify40.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0292541
11273493
25002491

prune180.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* x.im y.re) (* x.re y.im))
15.3b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.2b
(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))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* x.im y.re) (* x.re y.im))
109.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify99.0ms

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: 23.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
15.3b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
31.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
100×add-sqr-sqrt
98×add-cube-cbrt *-un-lft-identity
54×sqrt-prod
27×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
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 frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/l/
1×pow-flip inv-pow
Counts
4 → 193
Calls
4 calls:
13.0ms
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
9.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
80.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify74.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05742905
124492677
250022540

prune416.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.2b
(- (* x.im y.re) (* x.re y.im))
0.5b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
25.9b
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×add-cube-cbrt times-frac
17×add-exp-log
15×associate-*r*
11×add-cbrt-cube
8×add-log-exp
7×pow1
4×div-exp prod-exp associate-/r/
3×flip3-- flip3-+ associate-*l* associate-/r* flip-- flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×+-commutative sub-neg pow-flip frac-2neg diff-log associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 98
Calls
4 calls:
2.0ms
(+ (* y.re y.re) (* y.im y.im))
5.0ms
(- (* x.im y.re) (* x.re y.im))
5.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
20.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series181.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* y.re y.re) (* y.im y.im))
34.0ms
(- (* x.im y.re) (* x.re y.im))
39.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
80.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify51.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0384857
11929753
25002724

prune216.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.7b

regimes132.0ms

Accuracy

0% (3.1b remaining)

Error of 26.8b against oracle of 23.7b and baseline of 26.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02014
12014

end0.0ms

sample974.0ms

Algorithm
intervals
Results
754.0ms8429×body80valid