Details

Time bar (total: 10.2s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify78.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize15.0ms

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)))

rewrite633.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
586×*-un-lft-identity
340×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 associate-/l/
3×frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 465
Calls
4 calls:
53.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
164.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
245.0ms
(/ (/ (/ (+ (+ (+ 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))
141.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
131.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
144.0ms
(/ (/ (/ (+ (+ (+ 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))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify131.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
0149213034
1500212552

prune938.0ms

Filtered
477 candidates to 281 candidates (58.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

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

rewrite510.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
56×add-sqr-sqrt
46×times-frac
45×sqrt-prod
38×add-cube-cbrt
27×associate-*r*
11×add-exp-log add-cbrt-cube
10×sqrt-div distribute-lft-out
8×pow1
7×flip3-+ associate-*l* flip-+ associate-/l*
6×unswap-sqr
4×associate-/r/ add-log-exp
3×associate-/r*
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 137
Calls
4 calls:
105.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
281.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
59.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
59.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series351.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
74.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
45.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify70.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05032153
120641923
250011855

prune369.0ms

Filtered
149 candidates to 98 candidates (65.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize15.0ms

Local error

Found 4 expressions with local error:

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)))
14.7b
(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)))
14.7b
(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)))

rewrite700.0ms

Algorithm
rewrite-expression-head
Rules
1236×times-frac
888×*-un-lft-identity
508×add-sqr-sqrt
492×sqrt-prod
488×add-cube-cbrt
200×distribute-lft-out
72×associate-/r/
38×flip3-+ flip-+
36×div-inv
8×add-exp-log rem-sqrt-square add-cbrt-cube associate-/l*
6×pow1 associate-/r*
4×associate-/l/ add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 590
Calls
4 calls:
139.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
139.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
184.0ms
(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)))
184.0ms
(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)))

series720.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
281.0ms
(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)))
289.0ms
(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)))

simplify197.0ms

Algorithm
egg-herbie
Counts
602 → 602
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
0158020724
1500120206

prune1.6s

Filtered
602 candidates to 320 candidates (53.2%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize25.0ms

Local error

Found 4 expressions with local error:

3.1b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.7b
(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)))
14.7b
(sqrt (/ (/ (* (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

rewrite640.0ms

Algorithm
rewrite-expression-head
Rules
655×times-frac
471×*-un-lft-identity
288×sqrt-prod
270×add-sqr-sqrt
257×add-cube-cbrt
107×distribute-lft-out
44×associate-/r/
24×flip3-+ flip-+
22×div-inv
8×cbrt-prod
6×pow1 rem-sqrt-square
4×add-exp-log cbrt-div add-cbrt-cube add-log-exp
2×sqrt-pow1 pow1/2 pow1/3 sqrt-div
Counts
4 → 342
Calls
4 calls:
31.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
29.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
181.0ms
(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)))
373.0ms
(sqrt (/ (/ (* (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

series688.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
62.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
280.0ms
(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)))
286.0ms
(sqrt (/ (/ (* (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

simplify145.0ms

Algorithm
egg-herbie
Counts
354 → 354
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0173313136
1500112730

prune1.3s

Filtered
354 candidates to 207 candidates (58.5%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.9b

regimes114.0ms

Accuracy

82.2% (0.5b remaining)

Error of 1.7b against oracle of 1.2b and baseline of 3.8b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04356
14356

end0.0ms

sample521.0ms

Algorithm
intervals
Results
290.0ms8000×body80valid
93.0ms8000×pre80true