Details

Time bar (total: 4.0s)

sample28.0ms

Algorithm
intervals
Results
6.0ms183×body80valid
5.0ms28×body2560valid
3.0ms12×body5120valid
3.0ms15×body1280valid
1.0ms10×body640valid
0.0ms4×body320valid
0.0ms4×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0248
1308
2338
3338

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.1b
(+ (sqrt (+ (* re re) (* im im))) re)
32.6b
(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
7×pow1 add-sqr-sqrt sqrt-prod
6×add-cube-cbrt fma-def
5×add-log-exp
4×sqrt-div
3×add-exp-log expm1-log1p-u sqrt-pow1 flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square pow-prod-down sum-log hypot-def distribute-lft-out
Counts
3 → 53
Calls
3 calls:
11.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
16.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series283.0ms

Counts
3 → 9
Calls
3 calls:
194.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
51.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify76.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0264372
1830337
22660322
35002320

prune204.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot re im)
0.3b
(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
1.3b
(+ (* 1 (hypot re im)) re)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1
5×add-log-exp
4×*-un-lft-identity
3×add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt 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 distribute-lft-out
Counts
3 → 40
Calls
3 calls:
1.0ms
(hypot re im)
8.0ms
(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
3.0ms
(+ (* 1 (hypot re im)) re)

series301.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(hypot re im)
195.0ms
(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
55.0ms
(+ (* 1 (hypot re im)) re)

simplify75.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0219232
1647208
22702200
35001199

prune160.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot re im)
0.0b
(sqrt (+ (* 1 (hypot re im)) re))
0.4b
(* (sqrt 2.0) (sqrt (+ (* 1 (hypot re im)) re)))
1.3b
(+ (* 1 (hypot re im)) re)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×sqrt-prod
12×*-un-lft-identity
9×pow1 add-cube-cbrt
7×associate-*r*
6×add-exp-log 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-+ distribute-lft-out
2×associate-*r/
1×+-commutative rem-sqrt-square hypot-udef fma-def sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod
Counts
4 → 78
Calls
4 calls:
0.0ms
(hypot re im)
4.0ms
(sqrt (+ (* 1 (hypot re im)) re))
14.0ms
(* (sqrt 2.0) (sqrt (+ (* 1 (hypot re im)) re)))
3.0ms
(+ (* 1 (hypot re im)) re)

series428.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(hypot re im)
130.0ms
(sqrt (+ (* 1 (hypot re im)) re))
192.0ms
(* (sqrt 2.0) (sqrt (+ (* 1 (hypot re im)) re)))
60.0ms
(+ (* 1 (hypot re im)) re)

simplify39.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0325527
11121472
25002462

prune272.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (hypot re im) re))
0.2b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re))))
0.3b
(* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re)))
1.3b
(+ (hypot re im) re)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
35×sqrt-prod
29×add-sqr-sqrt
20×*-un-lft-identity
18×associate-*l*
17×pow1
14×add-cube-cbrt
11×add-exp-log add-cbrt-cube
10×pow-prod-down
8×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×fma-def sqrt-unprod distribute-lft-out
2×*-commutative
1×+-commutative rem-sqrt-square sum-log hypot-def
Counts
4 → 107
Calls
4 calls:
4.0ms
(sqrt (+ (hypot re im) re))
30.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re))))
16.0ms
(* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re)))
3.0ms
(+ (hypot re im) re)

series637.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(sqrt (+ (hypot re im) re))
196.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re))))
254.0ms
(* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re)))
55.0ms
(+ (hypot re im) re)

simplify47.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0404829
11592743
25001726

prune325.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.1b

regimes99.0ms

Accuracy

21.9% (4.7b remaining)

Error of 11.8b against oracle of 7.2b and baseline of 13.1b

bsearch133.0ms

Steps
ItersRangePoint
8
-4.877250012809174e+31
-3.3498184400795746e+28
-1.3113496370405717e+31
5
-4.4598663129175566e+213
-1.3314668636243889e+213
-3.2591409009285863e+213
7
-8.372319345062302e+230
-6.820094116973909e+228
-7.314302479759499e+228

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04530
14930
24930

end0.0ms

sample676.0ms

Algorithm
intervals
Results
195.0ms6012×body80valid
127.0ms635×body2560valid
89.0ms337×body5120valid
73.0ms466×body1280valid
37.0ms299×body640valid
14.0ms147×body320valid
6.0ms104×body160valid