Details

Time bar (total: 4.4s)

sample25.0ms

Algorithm
intervals
Results
6.0ms190×body80valid
3.0ms16×body2560valid
2.0ms15×body1280valid
2.0ms8×body5120valid
2.0ms14×body640valid
1.0ms8×body320valid
0.0ms5×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0178
1248
2308
3358
4358

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.8b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.3b
(- (sqrt (+ (* re re) (* im im))) re)
28.7b
(sqrt (+ (* re re) (* im im)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
25×sqrt-prod
22×add-sqr-sqrt
11×associate-*l*
10×distribute-lft-out
8×pow1 add-cube-cbrt add-log-exp
6×associate-*r*
4×add-exp-log sqrt-div swap-sqr add-cbrt-cube difference-of-squares
3×rem-sqrt-square sqrt-pow1
2×flip3-- flip3-+ pow1/2 associate-*r/ flip-- flip-+ distribute-lft-out-- unswap-sqr
1×+-commutative sub-neg diff-log pow-prod-down sum-log *-commutative
Counts
4 → 80
Calls
4 calls:
15.0ms
(+ (* re re) (* im im))
23.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
20.0ms
(- (sqrt (+ (* re re) (* im im))) re)
18.0ms
(sqrt (+ (* re re) (* im im)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* re re) (* im im))
182.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms
(- (sqrt (+ (* re re) (* im im))) re)
41.0ms
(sqrt (+ (* re re) (* im im)))

simplify106.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0297669
11079632
23788622
35001621

prune181.0ms

Filtered
92 candidates to 63 candidates (68.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New85792
Fresh000
Picked101
Done000
Total86793

Merged error: 16.6b

Counts
93 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.0b
(sqrt (* 2.0 (- (sqrt (pow (+ (* re re) (* im im)) 1)) re)))
1.3b
(- (sqrt (pow (+ (* re re) (* im im)) 1)) re)
28.7b
(sqrt (pow (+ (* re re) (* im im)) 1))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
35×sqrt-prod
31×add-sqr-sqrt
11×unpow-prod-down associate-*l*
10×add-cube-cbrt distribute-lft-out
9×pow1
8×sqrt-pow1 associate-*r* add-log-exp difference-of-squares
5×rem-sqrt-square
4×add-exp-log swap-sqr add-cbrt-cube sqr-pow
3×pow-unpow
2×flip3-- pow1/2 sqrt-div associate-*r/ flip-- distribute-lft-out-- unswap-sqr
1×+-commutative sub-neg pow-pow flip3-+ diff-log pow-prod-down sum-log *-commutative flip-+
Counts
4 → 93
Calls
4 calls:
15.0ms
(+ (* re re) (* im im))
28.0ms
(sqrt (* 2.0 (- (sqrt (pow (+ (* re re) (* im im)) 1)) re)))
21.0ms
(- (sqrt (pow (+ (* re re) (* im im)) 1)) re)
16.0ms
(sqrt (pow (+ (* re re) (* im im)) 1))

series307.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* re re) (* im im))
184.0ms
(sqrt (* 2.0 (- (sqrt (pow (+ (* re re) (* im im)) 1)) re)))
52.0ms
(- (sqrt (pow (+ (* re re) (* im im)) 1)) re)
37.0ms
(sqrt (pow (+ (* re re) (* im im)) 1))

simplify41.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0353808
11289739
25002729

prune189.0ms

Filtered
105 candidates to 65 candidates (61.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1023105
Fresh336
Picked011
Done000
Total1057112

Merged error: 16.6b

Counts
112 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (pow (+ (* re re) (* im im)) 1/2) re)
4.3b
(sqrt (* 2.0 (/ (+ (pow im 2) 0) (+ (pow (+ (* re re) (* im im)) 1/2) re))))
22.5b
(/ (+ (pow im 2) 0) (+ (pow (+ (* re re) (* im im)) 1/2) re))
28.7b
(pow (+ (* re re) (* im im)) 1/2)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
86×*-un-lft-identity
40×add-sqr-sqrt
34×times-frac
32×sqrt-prod
29×add-cube-cbrt
27×distribute-lft-out
22×associate-*r*
16×sqrt-div
13×associate-*r/
10×associate-/l*
8×pow1 unpow-prod-down associate-/r*
7×add-exp-log associate-*l*
6×add-cbrt-cube add-log-exp
5×flip3-+ flip-+
4×associate-/r/ associate-/l/ unswap-sqr
3×rem-sqrt-square pow-unpow clear-num un-div-inv
2×frac-2neg sqrt-pow1 swap-sqr div-inv
1×cbrt-undiv +-commutative pow-to-exp pow-pow pow1/2 div-exp pow-prod-down pow-exp sum-log *-commutative unpow1/2 sqr-pow
Counts
4 → 136
Calls
4 calls:
20.0ms
(+ (pow (+ (* re re) (* im im)) 1/2) re)
36.0ms
(sqrt (* 2.0 (/ (+ (pow im 2) 0) (+ (pow (+ (* re re) (* im im)) 1/2) re))))
26.0ms
(/ (+ (pow im 2) 0) (+ (pow (+ (* re re) (* im im)) 1/2) re))
16.0ms
(pow (+ (* re re) (* im im)) 1/2)

series362.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(+ (pow (+ (* re re) (* im im)) 1/2) re)
152.0ms
(sqrt (* 2.0 (/ (+ (pow im 2) 0) (+ (pow (+ (* re re) (* im im)) 1/2) re))))
76.0ms
(/ (+ (pow im 2) 0) (+ (pow (+ (* re re) (* im im)) 1/2) re))
69.0ms
(pow (+ (* re re) (* im im)) 1/2)

simplify89.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05371726
125121625
250021619

prune328.0ms

Filtered
148 candidates to 101 candidates (68.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1426148
Fresh325
Picked101
Done101
Total1478155

Merged error: 12.8b

Counts
155 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ im (/ (+ (pow (+ (* re re) (* im im)) 1/2) re) im))
1.2b
(+ (pow (+ (* re re) (* im im)) 1/2) re)
4.3b
(sqrt (* 2.0 (* 1 (/ im (/ (+ (pow (+ (* re re) (* im im)) 1/2) re) im)))))
28.7b
(pow (+ (* re re) (* im im)) 1/2)

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
210×times-frac
193×*-un-lft-identity
188×add-sqr-sqrt
144×associate-*r*
113×add-cube-cbrt
97×sqrt-prod
46×associate-*r/
42×unswap-sqr
38×associate-/r*
32×distribute-lft-out
30×associate-/r/
26×sqrt-div
22×associate-/l*
11×pow1
10×add-exp-log rem-sqrt-square associate-*l* div-inv
9×add-cbrt-cube
8×unpow-prod-down
6×clear-num un-div-inv add-log-exp
4×frac-2neg associate-/l/
3×cbrt-undiv pow-unpow sqrt-pow1 flip3-+ div-exp pow-prod-down flip-+
2×swap-sqr *-commutative
1×+-commutative pow-to-exp pow-pow pow1/2 pow-exp sum-log unpow1/2 sqr-pow
Counts
4 → 272
Calls
4 calls:
30.0ms
(/ im (/ (+ (pow (+ (* re re) (* im im)) 1/2) re) im))
20.0ms
(+ (pow (+ (* re re) (* im im)) 1/2) re)
65.0ms
(sqrt (* 2.0 (* 1 (/ im (/ (+ (pow (+ (* re re) (* im im)) 1/2) re) im)))))
16.0ms
(pow (+ (* re re) (* im im)) 1/2)

series373.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ im (/ (+ (pow (+ (* re re) (* im im)) 1/2) re) im))
66.0ms
(+ (pow (+ (* re re) (* im im)) 1/2) re)
158.0ms
(sqrt (* 2.0 (* 1 (/ im (/ (+ (pow (+ (* re re) (* im im)) 1/2) re) im)))))
69.0ms
(pow (+ (* re re) (* im im)) 1/2)

simplify73.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012413865
150013697

prune544.0ms

Filtered
284 candidates to 177 candidates (62.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2786284
Fresh527
Picked011
Done000
Total2839292

Merged error: 8.2b

Counts
292 → 9

regimes131.0ms

Accuracy

52.5% (13.0b remaining)

Error of 23.1b against oracle of 10.1b and baseline of 37.4b

bsearch183.0ms

Steps
ItersRangePoint
8
5.360415289181945e+152
1.3892773783954416e+156
1.338656002245574e+154
7
2.8231387681942284e-225
7.358046812615038e-224
7.222181096583517e-225
8
-1.8208622260955044e-231
-6.0728879748155805e-236
-8.120321757998124e-235
8
-3.3937628526691897e-46
-5.9247096471480265e-50
-8.95791604585242e-50

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07842
18642
28642

end0.0ms

sample680.0ms

Algorithm
intervals
Results
209.0ms5986×body80valid
135.0ms695×body2560valid
86.0ms538×body1280valid
62.0ms264×body5120valid
38.0ms277×body640valid
15.0ms156×body320valid
5.0ms84×body160valid