Details

Time bar (total: 4.0s)

sample43.0ms

Algorithm
intervals
Results
12.0ms181×body80valid
10.0ms30×body2560valid
5.0ms18×body1280valid
3.0ms7×body5120valid
2.0ms11×body640valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0228
1248
2248

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.0b
(+ (sqrt (+ (* re re) (* im im))) re)
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×*-un-lft-identity
5×add-sqr-sqrt add-log-exp
4×add-cube-cbrt sqrt-div sqrt-prod
3×add-exp-log sqrt-pow1 flip3-+ add-cbrt-cube flip-+
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square pow-prod-down sum-log distribute-lft-out
Counts
3 → 40
Calls
3 calls:
11.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
14.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series253.0ms

Counts
3 → 9
Calls
3 calls:
170.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0244351
1743325
22278315
35001312

prune150.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
10.7b
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
26.6b
(sqrt (+ (* re re) (* im im)))
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
27.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series152.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
48.0ms
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
34.0ms
(sqrt (+ (* re re) (* im im)))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02671096
1974974
25001950

prune288.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b
(sqrt (* 2.0 (+ (pow (+ (* re re) (* im im)) (/ 1 2)) re)))
1.0b
(+ (pow (+ (* re re) (* im im)) (/ 1 2)) re)
26.6b
(pow (+ (* re re) (* im im)) (/ 1 2))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
13×pow-unpow *-un-lft-identity
11×add-sqr-sqrt add-cube-cbrt
9×times-frac
7×pow1
5×add-log-exp
4×add-exp-log
3×unpow-prod-down add-cbrt-cube
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×+-commutative pow-to-exp pow-pow pow1/2 pow-prod-down pow-exp sum-log sqrt-prod div-inv distribute-lft-out sqr-pow
Counts
3 → 52
Calls
3 calls:
18.0ms
(sqrt (* 2.0 (+ (pow (+ (* re re) (* im im)) (/ 1 2)) re)))
25.0ms
(+ (pow (+ (* re re) (* im im)) (/ 1 2)) re)
5.0ms
(pow (+ (* re re) (* im im)) (/ 1 2))

series262.0ms

Counts
3 → 9
Calls
3 calls:
134.0ms
(sqrt (* 2.0 (+ (pow (+ (* re re) (* im im)) (/ 1 2)) re)))
62.0ms
(+ (pow (+ (* re re) (* im im)) (/ 1 2)) re)
66.0ms
(pow (+ (* re re) (* im im)) (/ 1 2))

simplify108.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0298439
1986402
24211378
35002378

prune168.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (sqrt (+ (* re re) (* im im))) re)
7.1b
(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
17.7b
(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×pow1
7×add-cube-cbrt sqrt-prod
6×times-frac associate-/r* add-log-exp difference-of-squares
3×sqrt-pow1 sqrt-div distribute-lft-out--
2×cbrt-undiv flip3-- pow1/2 div-exp associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg flip3-+ diff-log associate-*r/ pow-prod-down prod-exp clear-num cbrt-unprod flip-+ div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
19.0ms
(- (sqrt (+ (* re re) (* im im))) re)
18.0ms
(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
21.0ms
(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms
(sqrt (+ (* re re) (* im im)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (sqrt (+ (* re re) (* im im))) re)
192.0ms
(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
74.0ms
(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0369696
11474620
25001611

prune208.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.2b

regimes178.0ms

Accuracy

58.8% (10.1b remaining)

Error of 24.3b against oracle of 14.2b and baseline of 38.8b

bsearch314.0ms

Steps
ItersRangePoint
9
5.0931338003169406e+64
1.1608947055862536e+73
4.088444381602303e+68
10
1.4010557473267428e-242
1.7800473162436263e-231
1.4179378703523445e-242
9
-3.3653750376489624e-125
-4.187437093510799e-132
-3.312429260003495e-125
9
-2.660191539110354e-86
-6.01839662165218e-93
-7.4245329977218585e-93
10
-1.0086918763639924e+156
-1.3734446941131454e+138
-1.3473850118088864e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07744
17744

end0.0ms

sample1.1s

Algorithm
intervals
Results
419.0ms6082×body80valid
234.0ms683×body2560valid
133.0ms479×body1280valid
105.0ms261×body5120valid
60.0ms255×body640valid
29.0ms162×body320valid
9.0ms78×body160valid