Details

Time bar (total: 12.0s)

sample27.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify89.0ms

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: 2.6b

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))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

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:
120.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
333.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
487.0ms
(/ (/ (/ (+ (+ (+ 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))
288.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
136.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
140.0ms
(/ (/ (/ (+ (+ (+ 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))
72.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify139.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0151312983
1500212137

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.4b

localize16.0ms

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))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite998.0ms

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:
10.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
398.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
285.0ms
(/ (* (/ (+ (+ (+ 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))
290.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
142.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
153.0ms
(/ (* (/ (+ (+ (+ 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))
72.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify70.0ms

Algorithm
egg-herbie
Counts
302 → 302
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012994373
150013561

prune689.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.2b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
407×times-frac
391×*-un-lft-identity
293×sqrt-prod
222×add-sqr-sqrt
198×add-cube-cbrt
110×associate-*l*
107×distribute-lft-out
31×associate-/r/
29×associate-/l*
19×flip3-+ flip-+
16×div-inv
15×add-exp-log add-cbrt-cube
12×associate-/r*
8×sqrt-div unswap-sqr
6×pow1 associate-*r*
5×associate-/l/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ prod-exp cbrt-unprod
1×sqrt-undiv pow-prod-down associate-*l/ *-commutative
Counts
4 → 389
Calls
4 calls:
473.0ms
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
264.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
284.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
286.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series587.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
180.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
72.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
74.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify153.0ms

Algorithm
egg-herbie
Counts
401 → 401
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
09938715
135788229
250018154

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.3b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite880.0ms

Algorithm
rewrite-expression-head
Rules
257×times-frac
245×*-un-lft-identity
220×sqrt-prod
144×add-sqr-sqrt
141×add-cube-cbrt
56×distribute-lft-out
30×associate-/l*
20×associate-/r/
16×associate-/r*
13×flip3-+ flip-+
10×add-exp-log add-cbrt-cube div-inv
7×sqrt-div
5×pow1 associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv frac-2neg div-exp clear-num
1×rem-sqrt-square sqrt-undiv sqrt-pow1 pow1/2 hypot-def
Counts
4 → 292
Calls
4 calls:
261.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
186.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
128.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
288.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series499.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
204.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
43.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
73.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify124.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
08706379
133195965
250025871

prune1.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.4b

regimes80.0ms

Accuracy

54.6% (1.2b remaining)

Error of 2.5b against oracle of 1.3b and baseline of 4.0b

bsearch70.0ms

Steps
ItersRangePoint
10
7.430420921431803e+162
2.7887037251969743e+180
8.455186641284007e+162

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03327
13327

end0.0ms

sample543.0ms

Algorithm
intervals
Results
274.0ms8000×body80valid
89.0ms8000×pre80true