Details

Time bar (total: 10.4s)

sample34.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
4.0ms256×pre80true

simplify85.0ms

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 3 expressions with local error:

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)))

rewrite626.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
583×*-un-lft-identity
339×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
19×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
4×associate-/l/
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
Counts
3 → 456
Calls
3 calls:
178.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
265.0ms
(/ (/ (/ (+ (+ (+ 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))
151.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series371.0ms

Counts
3 → 9
Calls
3 calls:
142.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms
(/ (/ (/ (+ (+ (+ 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))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify133.0ms

Algorithm
egg-herbie
Counts
465 → 465
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0145512992
1500112037

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
13.5b
(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

rewrite852.0ms

Algorithm
rewrite-expression-head
Rules
934×times-frac
557×*-un-lft-identity
429×add-sqr-sqrt
415×add-cube-cbrt
166×associate-*l*
71×distribute-lft-out
59×associate-/l*
49×add-exp-log add-cbrt-cube
32×div-inv
24×cbrt-undiv div-exp
16×associate-/r/
11×flip3-- flip--
10×associate-/r*
8×prod-diff prod-exp cbrt-unprod associate-/l/
7×distribute-rgt-in distribute-lft-in
6×pow1
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u add-log-exp unswap-sqr
3×frac-2neg associate-*r* clear-num
2×sub-neg flip3-+ associate-*l/ associate--l+ flip-+
1×pow-prod-down *-commutative
Counts
4 → 522
Calls
4 calls:
187.0ms
(/ (* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
181.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
134.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
311.0ms
(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

series547.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
158.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
80.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
151.0ms
(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

simplify152.0ms

Algorithm
egg-herbie
Counts
534 → 534
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0205412731
1500212127

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
0.1b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
0.1b
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite559.0ms

Algorithm
rewrite-expression-head
Rules
196×times-frac
167×add-exp-log
145×add-sqr-sqrt
128×*-un-lft-identity
102×div-exp
100×add-cube-cbrt
61×add-cbrt-cube
44×associate-*r*
40×prod-exp
30×1-exp
29×cbrt-undiv
20×associate-/r*
18×associate-*l*
15×rec-exp
14×unswap-sqr
12×cbrt-unprod div-inv
9×distribute-lft-out
8×associate-/r/ associate-/l*
7×pow1
6×associate-/l/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/ un-div-inv
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 290
Calls
4 calls:
5.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
230.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
156.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
151.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
149.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
162.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify66.0ms

Algorithm
egg-herbie
Counts
302 → 302
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012994373
150013561

prune653.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
13.5b
(* (/ (/ (* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

rewrite779.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
62×times-frac
57×*-un-lft-identity
41×add-cube-cbrt
38×associate-*l*
29×add-exp-log sqrt-prod add-cbrt-cube
28×associate-*r*
10×pow1
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×sqrt-div prod-diff distribute-lft-out unswap-sqr
7×distribute-rgt-in distribute-lft-in
6×associate-/r/
5×flip3-- flip-- div-inv
4×expm1-log1p-u frac-times flip3-+ flip-+ log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate--l+ *-commutative hypot-def
Counts
4 → 172
Calls
4 calls:
273.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
69.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
72.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
358.0ms
(* (/ (/ (* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
51.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
146.0ms
(* (/ (/ (* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

simplify135.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08873733
147702838
250012838

prune573.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

regimes68.0ms

Accuracy

54.1% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.8b

bsearch64.0ms

Steps
ItersRangePoint
8
1.2268313987753119e+163
1.4307608554167672e+166
6.9339256802819e+165

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03223
13223

end0.0ms

sample852.0ms

Algorithm
intervals
Results
567.0ms8000×body80valid
138.0ms8000×pre80true