Details

Time bar (total: 3.9s)

sample26.0ms

Algorithm
intervals
Results
6.0ms191×body80valid
4.0ms21×body2560valid
3.0ms11×body5120valid
2.0ms15×body1280valid
2.0ms12×body640valid
0.0ms5×body320valid
0.0ms1×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 38.5b

localize14.0ms

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)))
29.1b
(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

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))
16.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (* re re) (* im im))
43.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
174.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
34.0ms
(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0296446
11086401
23561382
35001381

prune219.0ms

Filtered
79 candidates to 69 candidates (87.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.6b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1
5×*-un-lft-identity
4×associate-*r/ add-log-exp
3×add-sqr-sqrt add-cube-cbrt fma-def sqrt-pow1 pow-prod-down
2×add-exp-log expm1-log1p-u flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u
1×+-commutative pow1/2 sum-log sqrt-prod distribute-lft-out
Counts
2 → 33
Calls
2 calls:
3.0ms
(+ re (hypot re im))
11.0ms
(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))

series243.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(+ re (hypot re im))
184.0ms
(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))

simplify84.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0194185
1790167
23232161
35001161

prune110.0ms

Filtered
39 candidates to 33 candidates (84.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.3b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×*-un-lft-identity sqrt-prod
9×add-cube-cbrt
8×pow1
7×associate-*r*
6×associate-*l*
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div unswap-sqr
3×expm1-log1p-u fma-def sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ log1p-expm1-u distribute-lft-out
2×associate-*r/
1×+-commutative rem-sqrt-square sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod hypot-def
Counts
3 → 71
Calls
3 calls:
4.0ms
(sqrt (+ re (hypot re im)))
3.0ms
(+ re (hypot re im))
14.0ms
(* (sqrt 2.0) (sqrt (+ re (hypot re im))))

series364.0ms

Counts
3 → 9
Calls
3 calls:
120.0ms
(sqrt (+ re (hypot re im)))
59.0ms
(+ re (hypot re im))
185.0ms
(* (sqrt 2.0) (sqrt (+ re (hypot re im))))

simplify108.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0288432
1992402
24306387
35001387

prune203.0ms

Filtered
80 candidates to 62 candidates (77.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.3b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
19×pow1
18×add-exp-log
17×*-un-lft-identity
16×sqrt-prod
11×add-cube-cbrt add-cbrt-cube
10×cbrt-prod associate-*l*
9×pow-prod-down prod-exp cbrt-unprod
8×associate-*r*
6×sqrt-div associate-*r/ add-log-exp unswap-sqr
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×fma-def distribute-lft-out
2×*-commutative
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log hypot-def
Counts
4 → 99
Calls
4 calls:
4.0ms
(sqrt (+ re (hypot re im)))
3.0ms
(+ re (hypot re im))
18.0ms
(* (cbrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
30.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))

series787.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(sqrt (+ re (hypot re im)))
59.0ms
(+ re (hypot re im))
415.0ms
(* (cbrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
192.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0448927
11707772
25001711

prune295.0ms

Filtered
111 candidates to 82 candidates (73.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.3b

regimes86.0ms

Accuracy

13.4% (5.1b remaining)

Error of 12.2b against oracle of 7.2b and baseline of 13.0b

bsearch125.0ms

Steps
ItersRangePoint
4
-1.9588416456765557e-44
-1.3348717398520116e-44
-1.7053538714353348e-44
7
-4.681382254395288e+160
-2.578903516527549e+158
-1.1569629420680933e+160
8
-1.2809932923198163e+229
-5.300960546717222e+224
-1.9925944918866933e+225

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
04028
14714
25014
35014

end0.0ms

sample672.0ms

Algorithm
intervals
Results
201.0ms6072×body80valid
142.0ms703×body2560valid
77.0ms465×body1280valid
68.0ms263×body5120valid
36.0ms291×body640valid
12.0ms123×body320valid
5.0ms83×body160valid