Details

Time bar (total: 9.7s)

sample37.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
5.0ms256×pre80true

simplify88.0ms

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: 3.8b

localize17.0ms

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))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite626.0ms

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))
172.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
258.0ms
(/ (/ (/ (+ (+ (+ 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))
145.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
147.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
157.0ms
(/ (/ (/ (+ (+ (+ 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))
74.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify137.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0153413079
1500112129

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
0.2b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (+ (+ (fma alpha beta beta) alpha) 1.0))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
967×times-frac
486×*-un-lft-identity
426×add-sqr-sqrt add-cube-cbrt
402×sqrt-prod
182×associate-/l*
79×add-exp-log
49×associate-/r/ add-cbrt-cube
47×div-exp
46×sqrt-div
36×distribute-lft-out
26×cbrt-undiv
25×flip3-+ flip-+ div-inv
18×associate-/r*
13×pow1
10×prod-exp
8×pow-flip
6×cbrt-unprod pow-div
5×rec-exp sqrt-pow1 pow1/2 1-exp
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
2×inv-pow
1×associate-*l/
Counts
4 → 642
Calls
4 calls:
104.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
53.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
18.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
44.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (+ (+ (fma alpha beta beta) alpha) 1.0))

series398.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
38.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
71.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
104.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (+ (+ (fma alpha beta beta) alpha) 1.0))

simplify164.0ms

Algorithm
egg-herbie
Counts
654 → 654
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0194314792
1500213258

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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)) (fma 1.0 2.0 (+ alpha beta)))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite503.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
44×add-sqr-sqrt
42×times-frac
40×sqrt-prod
38×add-cube-cbrt
14×associate-/l*
10×distribute-lft-out
8×add-exp-log sqrt-div add-cbrt-cube
6×pow1 associate-/r*
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num associate-/r/ hypot-def div-inv
Counts
4 → 134
Calls
4 calls:
112.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
97.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
218.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
70.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series483.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
195.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
50.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify51.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04381734
113521629
250021603

prune486.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite421.0ms

Algorithm
rewrite-expression-head
Rules
782×sqrt-prod
690×times-frac
484×*-un-lft-identity
347×add-sqr-sqrt
338×add-cube-cbrt
73×distribute-lft-out
54×sqrt-div
36×associate-/r*
23×associate-/r/
15×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×add-exp-log add-cbrt-cube
7×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp hypot-def
2×associate-/l/
1×frac-2neg clear-num
Counts
4 → 482
Calls
4 calls:
177.0ms
(/ (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))))
68.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
67.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
70.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series345.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(/ (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))))
46.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify139.0ms

Algorithm
egg-herbie
Counts
494 → 494
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0105014171
1500112547

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

54% (1.6b remaining)

Error of 1.7b against oracle of 0.1b and baseline of 3.6b

bsearch37.0ms

Steps
ItersRangePoint
4
3.7543836586760903e+136
5.451806686237662e+136
5.370718961100869e+136

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04541
14541

end0.0ms

sample947.0ms

Algorithm
intervals
Results
650.0ms8000×body80valid
147.0ms8000×pre80true