Details

Time bar (total: 4.1s)

sample24.0ms

Algorithm
intervals
Results
6.0ms195×body80valid
4.0ms19×body2560valid
2.0ms16×body1280valid
2.0ms9×body5120valid
1.0ms12×body640valid
0.0ms5×body320valid

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: 39.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.1b
(+ (sqrt (+ (* re re) (* im im))) re)
0.2b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
30.5b
(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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:
4.0ms
(+ (* re re) (* im im))
7.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* re re) (* im im))
44.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
176.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (86.0ms)

IterNodesCost
0296446
11086401
23561382
35001381

prune224.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot re im)
0.1b
(+ (* (sqrt 1) (hypot re im)) re)
0.2b
(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))

rewrite13.0ms

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:
1.0ms
(hypot re im)
5.0ms
(+ (* (sqrt 1) (hypot re im)) re)
6.0ms
(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))

series294.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(hypot re im)
61.0ms
(+ (* (sqrt 1) (hypot re im)) re)
189.0ms
(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))

simplify72.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0218274
1658245
22414237
35001233

prune165.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot re im)
0.0b
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
0.1b
(+ (* (sqrt 1) (hypot re im)) re)
0.4b
(* (sqrt 2.0) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))

rewrite26.0ms

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:
1.0ms
(hypot re im)
5.0ms
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
5.0ms
(+ (* (sqrt 1) (hypot re im)) re)
14.0ms
(* (sqrt 2.0) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(hypot re im)
124.0ms
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
61.0ms
(+ (* (sqrt 1) (hypot re im)) re)
194.0ms
(* (sqrt 2.0) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))

simplify40.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0322609
11121566
25001552

prune451.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
0.1b
(+ (* (sqrt 1) (hypot re im)) re)
0.2b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re))))
0.3b
(* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))

rewrite40.0ms

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:
5.0ms
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
5.0ms
(+ (* (sqrt 1) (hypot re im)) re)
14.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re))))
14.0ms
(* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))

series607.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
61.0ms
(+ (* (sqrt 1) (hypot re im)) re)
186.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re))))
238.0ms
(* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))

simplify54.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04231053
11694954
25002938

prune332.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.9b

regimes144.0ms

Accuracy

33.2% (4.4b remaining)

Error of 11.6b against oracle of 7.2b and baseline of 13.8b

bsearch34.0ms

Steps
ItersRangePoint
6
-1.0806682141483241
-0.09277936894296426
-0.4962378853117394

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03316
13516
23516

end0.0ms

sample653.0ms

Algorithm
intervals
Results
202.0ms5992×body80valid
122.0ms655×body2560valid
80.0ms528×body1280valid
66.0ms288×body5120valid
34.0ms290×body640valid
18.0ms174×body320valid
4.0ms73×body160valid