Details

Time bar (total: 9.9s)

sample26.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
6.0ms256×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: 3.1b

localize11.0ms

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))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite677.0ms

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:
63.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
183.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
254.0ms
(/ (/ (/ (+ (+ (+ 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))
142.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
135.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify141.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0151312983
1500212137

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
0.1b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
0.1b
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite522.0ms

Algorithm
rewrite-expression-head
Rules
196×times-frac
167×add-exp-log
145×add-sqr-sqrt
128×*-un-lft-identity
102×div-exp
100×add-cube-cbrt
61×add-cbrt-cube
44×associate-*r*
40×prod-exp
30×1-exp
29×cbrt-undiv
20×associate-/r*
18×associate-*l*
15×rec-exp
14×unswap-sqr
12×cbrt-unprod div-inv
9×distribute-lft-out
8×associate-/r/ associate-/l*
7×pow1
6×associate-/l/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/ un-div-inv
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 290
Calls
4 calls:
5.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
213.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
145.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
145.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
151.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
161.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify71.0ms

Algorithm
egg-herbie
Counts
302 → 302
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012994378
150013561

prune648.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (/ (+ (+ (+ 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))
0.3b
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite936.0ms

Algorithm
rewrite-expression-head
Rules
484×times-frac
370×*-un-lft-identity
302×sqrt-prod
284×add-sqr-sqrt
224×add-cube-cbrt
83×swap-sqr
64×distribute-lft-out
63×associate-*r* associate-*l*
38×associate-/r/
21×flip3-+ flip-+
19×pow1 div-inv
16×unswap-sqr
15×add-exp-log add-cbrt-cube
10×associate-/r*
9×associate-/l*
8×sqrt-pow1 pow1/2 sqrt-div
7×associate-/l/
5×pow-prod-up
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg pow-prod-down clear-num pow-sqr
2×frac-times associate-*r/ associate-*l/ prod-exp cbrt-unprod
1×pow2 pow-plus sqrt-unprod rem-square-sqrt *-commutative
Counts
4 → 359
Calls
4 calls:
168.0ms
(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (/ (+ (+ (+ 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))
453.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
141.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
144.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (/ (+ (+ (+ 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))
146.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
71.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify255.0ms

Algorithm
egg-herbie
Counts
371 → 371
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
010598752
150018178

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite930.0ms

Algorithm
rewrite-expression-head
Rules
329×sqrt-prod
300×times-frac
203×*-un-lft-identity
171×associate-*r*
161×add-sqr-sqrt
155×add-cube-cbrt
24×distribute-lft-out
18×sqrt-div
16×associate-/r/
14×pow1
11×add-exp-log flip3-+ add-cbrt-cube flip-+
8×div-inv
7×pow-prod-down
5×frac-times sqrt-pow1 pow1/2 associate-*l/
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*r/ prod-exp associate-/r* cbrt-unprod
2×rem-sqrt-square sqrt-unprod hypot-def associate-/l/
1×cbrt-undiv frac-2neg div-exp associate-*l* clear-num *-commutative
Counts
4 → 273
Calls
4 calls:
629.0ms
(* (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))))
67.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
67.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
145.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))))
49.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
45.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify109.0ms

Algorithm
egg-herbie
Counts
285 → 285
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013519702
150029310

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

regimes70.0ms

Accuracy

55.1% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.6b

bsearch39.0ms

Steps
ItersRangePoint
5
1.2761513080479214e+167
3.467445464211409e+167
3.2116744201778903e+167

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03223
13223

end0.0ms

sample514.0ms

Algorithm
intervals
Results
282.0ms8000×body80valid
95.0ms8000×pre80true