Details

Time bar (total: 7.6s)

sample26.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
3.0ms256×pre80true

simplify83.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite610.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
587×*-un-lft-identity
341×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 475
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
167.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
251.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
143.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ alpha beta) (* beta alpha))
138.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
155.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify135.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0153413079
1500112129

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(/ (/ (+ (+ alpha (fma alpha beta beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ alpha (fma alpha beta beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.4b
(/ (+ (+ alpha (fma alpha beta beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite388.0ms

Algorithm
rewrite-expression-head
Rules
954×times-frac
835×*-un-lft-identity
388×add-sqr-sqrt add-cube-cbrt
254×distribute-lft-out
95×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 537
Calls
4 calls:
62.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
75.0ms
(/ (/ (+ (+ alpha (fma alpha beta beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
158.0ms
(/ (/ (/ (+ (+ alpha (fma alpha beta beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
50.0ms
(/ (+ (+ alpha (fma alpha beta beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
140.0ms
(/ (/ (+ (+ alpha (fma alpha beta beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
155.0ms
(/ (/ (/ (+ (+ alpha (fma alpha beta beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
81.0ms
(/ (+ (+ alpha (fma alpha beta beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify154.0ms

Algorithm
egg-herbie
Counts
549 → 549
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0151313903
1500213037

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)))
0.5b
(/ (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.3b
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))
3.3b
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
179×*-un-lft-identity
102×sqrt-prod
88×times-frac
72×distribute-lft-out
65×add-sqr-sqrt
59×add-cube-cbrt
14×associate-/r*
13×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
1×sqrt-undiv
Counts
4 → 192
Calls
4 calls:
51.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)))
42.0ms
(/ (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
21.0ms
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))
18.0ms
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))

series552.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)))
242.0ms
(/ (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
52.0ms
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))
47.0ms
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))

simplify72.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05262646
118932486
250012394

prune575.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
0.5b
(/ (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.3b
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))
3.3b
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
179×*-un-lft-identity
102×sqrt-prod
88×times-frac
72×distribute-lft-out
65×add-sqr-sqrt
59×add-cube-cbrt
16×associate-/l*
11×associate-/r*
10×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
1×sqrt-undiv
Counts
4 → 192
Calls
4 calls:
42.0ms
(/ (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
44.0ms
(/ (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
18.0ms
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))
18.0ms
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))

series353.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
111.0ms
(/ (sqrt (+ (+ alpha (fma alpha beta beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
47.0ms
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))
52.0ms
(sqrt (+ (+ alpha (fma alpha beta beta)) 1.0))

simplify73.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05262612
117522471
250032404

prune603.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.6b

regimes73.0ms

Accuracy

56% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch50.0ms

Steps
ItersRangePoint
8
6.080532357857461e+175
3.1725731237402986e+178
1.4955754255315103e+178

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02521
12521

end0.0ms

sample513.0ms

Algorithm
intervals
Results
272.0ms8000×body80valid
99.0ms8000×pre80true