Details

Time bar (total: 3.0s)

sample36.0ms

Algorithm
intervals
Results
17.0ms269×body80valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0197
1367
2487
3667
4727
5727

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.4b
(- (* x.im y.re) (* x.re y.im))
24.7b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

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))
2.0ms
(- (* 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)))

series149.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* y.re y.re) (* y.im y.im))
37.0ms
(- (* 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)))

simplify41.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0292541
11273493
25002491

prune166.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* x.im y.re) (* x.re y.im))
15.2b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

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:
2.0ms
(- (* 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))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* x.im y.re) (* x.re y.im))
164.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
54.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
44.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0304910
1990857
23354845
35001845

prune264.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
14.8b
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
18.3b
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt associate-/r/ add-log-exp
6×times-frac associate-/r*
5×flip3-+ flip-+
4×pow1 cbrt-undiv div-exp div-inv
3×distribute-rgt-out--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l*
1×+-commutative sub-neg flip3-- diff-log sum-log frac-sub flip-- distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 76
Calls
4 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
34.0ms
(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* y.re y.re) (* y.im y.im))
116.0ms
(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
45.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
42.0ms
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

simplify46.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0385746
11875664
25002660

prune221.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
18.3b
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
27.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.3b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite60.0ms

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:
42.0ms
(* (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
6.0ms
(/ (* x.im y.re) (+ (* 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)))

series161.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
41.0ms
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify61.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05761545
125941391
250011322

prune364.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.4b

regimes111.0ms

Accuracy

0% (1.1b remaining)

Error of 22.9b against oracle of 21.8b and baseline of 22.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01823
11823

end0.0ms

sample512.0ms

Algorithm
intervals
Results
299.0ms8514×body80valid