Details

Time bar (total: 4.6s)

sample49.0ms

Algorithm
intervals
Results
15.0ms181×body80valid
10.0ms28×body2560valid
6.0ms15×body5120valid
5.0ms18×body1280valid
2.0ms10×body640valid
0.0ms3×body160valid
0.0ms1×body320valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0248
1308
2338
3338

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.2b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.8b
(+ (sqrt (+ (* re re) (* im im))) re)
32.7b
(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
8×pow1 add-sqr-sqrt add-log-exp
7×add-cube-cbrt fma-def sqrt-prod
4×add-exp-log expm1-log1p-u flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u
3×sqrt-pow1
2×+-commutative pow1/2 associate-*r/ sum-log
1×rem-sqrt-square pow-prod-down hypot-def distribute-lft-out
Counts
4 → 67
Calls
4 calls:
3.0ms
(+ (* re re) (* im im))
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)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* re re) (* im im))
187.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
46.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
41.0ms
(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0296446
11086401
23561382
35001381

prune229.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot re im)
0.2b
(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
0.8b
(+ (* (sqrt 1) (hypot re im)) re)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1
5×add-log-exp
3×add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×+-commutative hypot-udef fma-def pow1/2 pow-prod-down sum-log sqrt-prod
Counts
3 → 39
Calls
3 calls:
0.0ms
(hypot re im)
5.0ms
(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
4.0ms
(+ (* (sqrt 1) (hypot re im)) re)

series313.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(hypot re im)
202.0ms
(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
64.0ms
(+ (* (sqrt 1) (hypot re im)) re)

simplify71.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0218274
1658245
22414237
35001233

prune159.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot re im)
0.0b
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
0.4b
(* (sqrt 2.0) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))
0.8b
(+ (* (sqrt 1) (hypot re im)) re)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×sqrt-prod
9×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×associate-*r/
1×+-commutative rem-sqrt-square hypot-udef fma-def sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod
Counts
4 → 75
Calls
4 calls:
0.0ms
(hypot re im)
6.0ms
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
20.0ms
(* (sqrt 2.0) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))
4.0ms
(+ (* (sqrt 1) (hypot re im)) re)

series449.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(hypot re im)
131.0ms
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
207.0ms
(* (sqrt 2.0) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))
58.0ms
(+ (* (sqrt 1) (hypot re im)) re)

simplify40.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0322609
11121566
25001552

prune262.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
0.2b
(* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))
0.2b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re))))
0.8b
(+ (* (sqrt 1) (hypot re im)) re)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
33×sqrt-prod
26×add-sqr-sqrt
18×associate-*l*
17×pow1
13×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
10×pow-prod-down
7×associate-*r*
6×sqrt-pow1 pow1/2 sqrt-div associate-*r/ add-log-exp unswap-sqr
4×expm1-log1p-u flip3-+ prod-exp cbrt-unprod flip-+ log1p-expm1-u
3×sqrt-unprod
2×*-commutative
1×+-commutative rem-sqrt-square fma-def sum-log
Counts
4 → 101
Calls
4 calls:
6.0ms
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
20.0ms
(* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))
29.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re))))
7.0ms
(+ (* (sqrt 1) (hypot re im)) re)

series674.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
268.0ms
(* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))
205.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re))))
63.0ms
(+ (* (sqrt 1) (hypot re im)) re)

simplify53.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04231053
11694954
25002938

prune345.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.4b

regimes81.0ms

Accuracy

30.4% (4.3b remaining)

Error of 11.7b against oracle of 7.5b and baseline of 13.6b

bsearch73.0ms

Steps
ItersRangePoint
9
-1.1902930357079885e-07
-5.549947570902944e-17
-5.386850751380747e-10

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03318
13518
23518

end0.0ms

sample1.2s

Algorithm
intervals
Results
423.0ms5987×body80valid
247.0ms673×body2560valid
146.0ms500×body1280valid
135.0ms312×body5120valid
68.0ms292×body640valid
29.0ms153×body320valid
10.0ms83×body160valid