Details

Time bar (total: 3.6s)

sample29.0ms

Algorithm
intervals
Results
6.0ms181×body80valid
6.0ms30×body2560valid
5.0ms12×body5120valid
3.0ms20×body1280valid
1.0ms7×body640valid
0.0ms3×body320valid
0.0ms3×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0248
1308
2338
3338

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize10.0ms

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)
31.0b
(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

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)))
15.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* re re) (* im im))
177.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms
(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0296446
11086401
23561382
35001381

prune231.0ms

Filtered
79 candidates to 69 candidates (87.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.6b

localize9.0ms

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)

series293.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(hypot re im)
189.0ms
(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
60.0ms
(+ (* (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

prune165.0ms

Filtered
48 candidates to 44 candidates (91.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot re im)
0.0b
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
0.3b
(* (sqrt 2.0) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))
0.8b
(+ (* (sqrt 1) (hypot re im)) re)

rewrite33.0ms

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))
21.0ms
(* (sqrt 2.0) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))
4.0ms
(+ (* (sqrt 1) (hypot re im)) re)

series421.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(hypot re im)
122.0ms
(sqrt (+ (* (sqrt 1) (hypot re im)) re))
194.0ms
(* (sqrt 2.0) (sqrt (+ (* (sqrt 1) (hypot re im)) re)))
55.0ms
(+ (* (sqrt 1) (hypot re im)) re)

simplify39.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0322609
11121566
25001552

prune266.0ms

Filtered
87 candidates to 72 candidates (82.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (hypot re im))
0.2b
(sqrt (* 2.0 (+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)))
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.7b
(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×pow1
22×sqrt-prod
13×add-cube-cbrt *-un-lft-identity
11×sqrt-pow1
10×pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube add-log-exp
5×pow-prod-up
4×expm1-log1p-u pow-prod-down log1p-expm1-u unswap-sqr
3×pow-sqr
2×flip3-+ sqrt-div associate-*r/ flip-+
1×+-commutative pow2 rem-sqrt-square fma-def pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
1.0ms
(sqrt (hypot re im))
17.0ms
(sqrt (* 2.0 (+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)))
7.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
15.0ms
(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

series387.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(sqrt (hypot re im))
194.0ms
(sqrt (* 2.0 (+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)))
44.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
61.0ms
(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

simplify45.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0339663
11250563
25002504

prune253.0ms

Filtered
107 candidates to 70 candidates (65.4%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.3b

regimes174.0ms

Accuracy

30.6% (4.2b remaining)

Error of 11.5b against oracle of 7.3b and baseline of 13.3b

bsearch52.0ms

Steps
ItersRangePoint
9
-1.746315848109072e-26
-3.537859505528638e-32
-6.718169998196866e-27

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03215
13415
23415

end0.0ms

sample660.0ms

Algorithm
intervals
Results
190.0ms6015×body80valid
128.0ms671×body2560valid
81.0ms491×body1280valid
73.0ms309×body5120valid
33.0ms269×body640valid
14.0ms153×body320valid
6.0ms92×body160valid