Details

Time bar (total: 3.7s)

sample29.0ms

Algorithm
intervals
Results
7.0ms182×body80valid
5.0ms24×body2560valid
4.0ms14×body5120valid
3.0ms19×body1280valid
1.0ms6×body640valid
1.0ms8×body320valid
0.0ms3×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0248
1308
2338
3338

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.8b
(+ (sqrt (+ (* re re) (* im im))) re)
30.8b
(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

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:
12.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
18.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series261.0ms

Counts
3 → 9
Calls
3 calls:
177.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
49.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0264372
1830337
22660322
35002320

prune181.0ms

Filtered
62 candidates to 56 candidates (90.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot re im)
0.1b
(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
0.8b
(+ (* 1 (hypot re im)) re)

rewrite8.0ms

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:
0.0ms
(hypot re im)
4.0ms
(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
3.0ms
(+ (* 1 (hypot re im)) re)

series300.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(hypot re im)
191.0ms
(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
59.0ms
(+ (* 1 (hypot re im)) re)

simplify76.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0219232
1647208
22702200
35001199

prune155.0ms

Filtered
49 candidates to 46 candidates (93.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (* 2.0 (* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))))
0.4b
(* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))
0.8b
(+ (* 1 (hypot re im)) re)
0.8b
(+ (* 1 (hypot re im)) re)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-div
25×pow1
24×add-sqr-sqrt
23×sqrt-prod
18×*-un-lft-identity
14×flip3-+ flip-+
12×add-cube-cbrt associate-*r/
11×sqrt-pow1
9×pow1/2 swap-sqr
8×frac-times add-log-exp
7×associate-*r* associate-*l*
6×add-exp-log pow-prod-down add-cbrt-cube distribute-lft-out
5×pow-prod-up
4×expm1-log1p-u associate-*l/ log1p-expm1-u unswap-sqr
3×pow-sqr
2×+-commutative fma-def sum-log
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 114
Calls
4 calls:
29.0ms
(sqrt (* 2.0 (* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))))
24.0ms
(* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))
3.0ms
(+ (* 1 (hypot re im)) re)
3.0ms
(+ (* 1 (hypot re im)) re)

series374.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(sqrt (* 2.0 (* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))))
55.0ms
(* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))
60.0ms
(+ (* 1 (hypot re im)) re)
60.0ms
(+ (* 1 (hypot re im)) re)

simplify50.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0325952
11146846
25001816

prune334.0ms

Filtered
126 candidates to 84 candidates (66.7%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (* 1 (hypot re im)) re))
0.8b
(+ (* 1 (hypot re im)) re)
0.8b
(+ (* 1 (hypot re im)) re)
0.8b
(+ (hypot re im) re)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-log-exp
6×add-sqr-sqrt add-cube-cbrt
5×fma-def
4×pow1 add-exp-log cbrt-prod expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
3×+-commutative sum-log
2×cbrt-div
1×pow1/3
Counts
4 → 63
Calls
4 calls:
3.0ms
(cbrt (+ (* 1 (hypot re im)) re))
3.0ms
(+ (* 1 (hypot re im)) re)
3.0ms
(+ (* 1 (hypot re im)) re)
3.0ms
(+ (hypot re im) re)

series324.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(cbrt (+ (* 1 (hypot re im)) re))
60.0ms
(+ (* 1 (hypot re im)) re)
60.0ms
(+ (* 1 (hypot re im)) re)
55.0ms
(+ (hypot re im) re)

simplify72.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0249335
1601305
22495302
35001296

prune351.0ms

Filtered
75 candidates to 70 candidates (93.3%)
Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 9.7b

regimes148.0ms

Accuracy

38.1% (3.9b remaining)

Error of 11.2b against oracle of 7.2b and baseline of 13.6b

bsearch58.0ms

Steps
ItersRangePoint
9
-7.149461396458222e+22
-5224788577222825.0
-3.741043568701442e+20

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02813
13013
23013

end0.0ms

sample735.0ms

Algorithm
intervals
Results
216.0ms5995×body80valid
156.0ms673×body2560valid
88.0ms505×body1280valid
71.0ms273×body5120valid
44.0ms302×body640valid
15.0ms149×body320valid
7.0ms103×body160valid