Details

Time bar (total: 7.9s)

sample24.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify85.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune11.0ms

Filtered
1 candidates to 1 candidates (100.0%)
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) (* 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))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite621.0ms

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)))
255.0ms
(/ (/ (/ (+ (+ (+ 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))
143.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (+ alpha beta) (* beta alpha))
282.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
159.0ms
(/ (/ (/ (+ (+ (+ 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))
86.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify141.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0153413079
1500112129

prune1.1s

Filtered
487 candidates to 297 candidates (61.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (log1p (expm1 (/ (/ (+ (+ (+ 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)))

rewrite389.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
113×*-un-lft-identity
73×add-sqr-sqrt add-cube-cbrt
25×associate-/l*
20×distribute-lft-out
14×associate-/r/
13×add-exp-log add-cbrt-cube
10×associate-/r*
8×flip3-+ flip-+
7×div-inv
5×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/l/
1×log1p-udef log1p-expm1
Counts
4 → 177
Calls
4 calls:
0.0ms
(log1p (expm1 (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
174.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
62.0ms
(/ (log1p (expm1 (/ (/ (+ (+ (+ 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)))

series635.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(log1p (expm1 (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
142.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
191.0ms
(/ (log1p (expm1 (/ (/ (+ (+ (+ 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)))

simplify95.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07053741
131283298
250013257

prune599.0ms

Filtered
189 candidates to 139 candidates (73.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
0.1b
(/ (log1p (expm1 (/ (/ 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.5b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
90×*-un-lft-identity
74×times-frac
73×add-exp-log
52×add-sqr-sqrt
47×add-cube-cbrt
43×div-exp
34×add-cbrt-cube
25×distribute-lft-out
21×associate-*l*
19×associate-/l*
16×prod-exp
15×1-exp
14×cbrt-undiv
10×associate-/r*
7×associate-/r/
6×pow1 rec-exp cbrt-unprod div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ associate-*r* clear-num flip-+
2×associate-*l/ fma-udef unswap-sqr
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/
Counts
4 → 186
Calls
4 calls:
37.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
16.0ms
(/ (/ 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
64.0ms
(/ (log1p (expm1 (/ (/ 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
15.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

series618.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
158.0ms
(/ (/ 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
204.0ms
(/ (log1p (expm1 (/ (/ 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
101.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify111.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08132755
145782360
250012358

prune565.0ms

Filtered
198 candidates to 118 candidates (59.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
0.1b
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ 1 (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))))
2.5b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
67×*-un-lft-identity
54×add-exp-log
34×times-frac add-cbrt-cube
32×add-sqr-sqrt
27×add-cube-cbrt
26×associate-*l*
24×distribute-lft-out
22×prod-exp
17×pow1
14×div-exp
12×cbrt-unprod
11×associate-*l/
9×associate-/r/
8×cbrt-undiv
7×pow-prod-down
6×flip3-+ associate-/r* flip-+ fma-udef associate-/l*
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u frac-times rec-exp 1-exp associate-*r* log1p-expm1-u add-log-exp
3×pow-flip div-inv
2×frac-2neg associate-*r/ clear-num *-commutative unswap-sqr
1×inv-pow
Counts
4 → 160
Calls
4 calls:
57.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
37.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
77.0ms
(/ 1 (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))))
15.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

series682.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
159.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
168.0ms
(/ 1 (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))))
104.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify102.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07052316
134691970
250011962

prune445.0ms

Filtered
172 candidates to 103 candidates (59.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

68.7% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 3.8b

bsearch72.0ms

Steps
ItersRangePoint
8
1.1016365673166607e+161
1.0797445965029766e+164
1.1125280590322559e+161

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04329
14329

end0.0ms

sample564.0ms

Algorithm
intervals
Results
316.0ms8000×body80valid
101.0ms8000×pre80true