Details

Time bar (total: 7.2s)

sample31.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
7.0ms256×pre80true

simplify83.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.1b

Counts
2 → 2

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

rewrite110.0ms

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:
8.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
39.0ms
(/ (/ (/ (+ (+ (+ 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))
14.0ms
(/ (+ (+ (+ 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)
137.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
147.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify145.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0151312983
1500212137

prune1.0s

Filtered
488 candidates to 299 candidates (61.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New4799488
Fresh101
Picked101
Done000
Total4819490

Merged error: 1.1b

Counts
490 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 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))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
126×*-un-lft-identity
84×sqrt-prod
77×times-frac
62×add-sqr-sqrt
56×add-cube-cbrt
39×distribute-lft-out
13×associate-/r*
12×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
1×sqrt-undiv
Counts
4 → 177
Calls
4 calls:
19.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
15.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series416.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
105.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
51.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05272718
119402545
250012473

prune501.0ms

Filtered
189 candidates to 109 candidates (57.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1890189
Fresh088
Picked011
Done000
Total1899198

Merged error: 1.1b

Counts
198 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
18.8b
(* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
171×times-frac
109×add-sqr-sqrt
106×*-un-lft-identity
96×add-cube-cbrt
54×add-exp-log
51×associate-*r*
34×add-cbrt-cube
26×div-exp
22×associate-/r/
19×associate-/l*
15×flip3-+ flip-+
14×cbrt-undiv
12×div-inv
10×pow1 prod-exp associate-/r*
6×cbrt-unprod associate-/l/
5×associate-*l* distribute-lft-out unswap-sqr
4×expm1-log1p-u frac-times rec-exp 1-exp associate-*l/ log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×pow-flip associate-*r/ inv-pow pow-div
1×pow-prod-down *-commutative
Counts
4 → 244
Calls
4 calls:
7.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
28.0ms
(/ (* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
33.0ms
(* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series402.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
54.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
159.0ms
(/ (* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
144.0ms
(* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify64.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
09963734
150023073

prune585.0ms

Filtered
256 candidates to 178 candidates (69.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2560256
Fresh077
Picked011
Done011
Total2569265

Merged error: 1.1b

Counts
265 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (fma 1.0 2.0 (+ alpha beta)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
3.2b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.2b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.2b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite392.0ms

Algorithm
rewrite-expression-head
Rules
651×times-frac
525×*-un-lft-identity
389×add-sqr-sqrt
291×cbrt-prod
258×add-cube-cbrt
194×associate-*l*
147×distribute-lft-out
141×associate-*r*
40×add-exp-log
28×add-cbrt-cube unswap-sqr
27×associate-/r/
20×cbrt-div
18×cbrt-undiv div-exp
16×flip3-+ flip-+
14×div-inv
9×prod-exp cbrt-unprod
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 443
Calls
4 calls:
328.0ms
(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (fma 1.0 2.0 (+ alpha beta)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series373.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (fma 1.0 2.0 (+ alpha beta)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
66.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify155.0ms

Algorithm
egg-herbie
Counts
455 → 455
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0182413521
1500213026

prune1.5s

Filtered
455 candidates to 324 candidates (71.2%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New4550455
Fresh066
Picked011
Done022
Total4559464

Merged error: 1.1b

Counts
464 → 9

regimes85.0ms

Accuracy

55.3% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch66.0ms

Steps
ItersRangePoint
9
4.876217483973988e+170
4.033142460877422e+176
7.924823143867044e+170

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03228
13228

end0.0ms

sample667.0ms

Algorithm
intervals
Results
375.0ms8000×body80valid
143.0ms8000×pre80true