Details

Time bar (total: 6.1s)

sample24.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify82.0ms

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) (* 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)))

rewrite122.0ms

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:
6.0ms
(+ (+ alpha beta) (* beta alpha))
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
42.0ms
(/ (/ (/ (+ (+ (+ 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)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
139.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
145.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify140.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0153413079
1500112129

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

localize15.0ms

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)))

rewrite55.0ms

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:
1.0ms
(log1p (expm1 (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
24.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
8.0ms
(/ (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))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series605.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(log1p (expm1 (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
135.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
182.0ms
(/ (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))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify93.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07053741
131283298
250013257

prune570.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize19.0ms

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 (* (/ (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 (* (/ (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))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
46×times-frac
40×add-sqr-sqrt
35×add-cube-cbrt
34×add-exp-log
25×distribute-lft-out
22×add-cbrt-cube
21×associate-*l*
12×div-exp
10×associate-/r*
9×pow1 associate-/l*
8×prod-exp
7×cbrt-undiv associate-/r/
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp frac-2neg flip3-+ 1-exp associate-*r* clear-num flip-+
2×pow-flip pow-prod-down associate-*l/ fma-udef unswap-sqr
1×distribute-rgt-in distribute-lft-in *-commutative inv-pow
Counts
4 → 153
Calls
4 calls:
11.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
10.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
8.0ms
(/ (log1p (expm1 (/ 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))
7.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

series575.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
144.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
188.0ms
(/ (log1p (expm1 (/ 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))
97.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify90.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
05952286
130501976
250011952

prune613.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
1.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
59×*-un-lft-identity
54×times-frac
34×add-sqr-sqrt
32×add-cube-cbrt
22×associate-/l*
20×add-exp-log add-cbrt-cube
14×distribute-lft-out
9×add-log-exp
8×associate-/r/
7×cbrt-undiv flip3-+ div-exp flip-+
6×pow1
5×associate-*l*
4×expm1-log1p-u fma-def associate-*l/ associate-/r* log1p-expm1-u div-inv
3×associate-*r* prod-exp sum-log cbrt-unprod associate-/l/
2×frac-2neg clear-num fma-udef
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 142
Calls
4 calls:
6.0ms
(+ (+ alpha beta) (* beta alpha))
8.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
21.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
17.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
36.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
165.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
74.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify99.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07082094
137541752
250011749

prune435.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes81.0ms

Accuracy

68.7% (1.2b remaining)

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

bsearch66.0ms

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

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04534
14534

end0.0ms

sample542.0ms

Algorithm
intervals
Results
302.0ms8000×body80valid
95.0ms8000×pre80true