Details

Time bar (total: 8.4s)

sample41.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
5.0ms256×pre80true

simplify84.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
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))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite678.0ms

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
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 → 476
Calls
4 calls:
64.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
175.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
260.0ms
(/ (/ (/ (+ (+ (+ 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))
147.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
137.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
153.0ms
(/ (/ (/ (+ (+ (+ 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))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify137.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0151312983
1500212137

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.4b

localize15.0ms

Local error

Found 3 expressions with local error:

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))) (* 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite540.0ms

Algorithm
rewrite-expression-head
Rules
354×times-frac
217×*-un-lft-identity
149×add-sqr-sqrt add-cube-cbrt
82×associate-/l*
40×add-exp-log
34×distribute-lft-out
31×add-cbrt-cube
30×associate-/r/
22×div-exp
16×cbrt-undiv flip3-+ flip-+
15×div-inv
7×associate-/r*
6×prod-exp
4×associate-/l/
3×pow1 expm1-log1p-u frac-2neg 1-exp clear-num cbrt-unprod log1p-expm1-u add-log-exp
2×associate-*r/
Counts
3 → 282
Calls
3 calls:
173.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
206.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (* 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
145.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series378.0ms

Counts
3 → 9
Calls
3 calls:
140.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
159.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (* 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify81.0ms

Algorithm
egg-herbie
Counts
291 → 291
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010856210
150015460

prune808.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (* 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
0.2b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
0.6b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.7b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
221×add-exp-log
210×times-frac
130×div-exp
103×*-un-lft-identity
94×add-cbrt-cube
83×add-sqr-sqrt add-cube-cbrt
63×associate-/l*
58×prod-exp
49×cbrt-undiv
48×sqrt-prod
29×associate-/r/
26×1-exp
22×sqrt-div
19×cbrt-unprod
13×rec-exp flip3-+ associate-/r* flip-+
12×distribute-lft-out
10×div-inv
8×associate-*r/
6×pow1 frac-times
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×pow-flip associate-*l/
2×associate-/l/
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 308
Calls
4 calls:
76.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (* 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
56.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
18.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
15.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

series511.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (* 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
164.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
70.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
98.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify87.0ms

Algorithm
egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013426277
150014665

prune883.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
17×*-un-lft-identity
12×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt
10×flip3-+ flip-+
9×add-exp-log
8×associate-/l/
7×add-cbrt-cube
6×times-frac associate-/r* sqrt-prod
4×pow1 expm1-log1p-u frac-times log1p-expm1-u add-log-exp
3×pow1/3 distribute-lft-out
2×cbrt-undiv sqrt-div associate-*r/ div-exp associate-*l/ associate-/r/
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 87
Calls
4 calls:
88.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
31.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
30.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
33.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series429.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
66.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
05241497
117551376
250011341

prune483.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

67.5% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 3.6b

bsearch77.0ms

Steps
ItersRangePoint
8
5.556773321411512e+173
1.60201838385931e+177
5.667473068272077e+173

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04439
14639
24639

end0.0ms

sample1.1s

Algorithm
intervals
Results
757.0ms8000×body80valid
145.0ms8000×pre80true