Details

Time bar (total: 8.8s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify83.0ms

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

localize15.0ms

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)))

rewrite609.0ms

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:
14.0ms
(+ (+ alpha beta) (* beta alpha))
167.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
249.0ms
(/ (/ (/ (+ (+ (+ 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)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
140.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
153.0ms
(/ (/ (/ (+ (+ (+ 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))
72.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify135.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0153413079
1500112129

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite721.0ms

Algorithm
rewrite-expression-head
Rules
214×times-frac
166×*-un-lft-identity
133×add-sqr-sqrt
112×add-cube-cbrt
61×add-exp-log add-cbrt-cube
54×associate-*l*
29×cbrt-undiv div-exp
27×distribute-lft-out
21×associate-/l*
15×associate-*r*
12×prod-exp cbrt-unprod div-inv
10×associate-/r*
8×associate-/r/
6×pow1 associate-/l/ unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ clear-num flip-+
2×frac-times flip3-- associate-*r/ associate-*l/ flip--
1×pow-prod-down *-commutative
Counts
4 → 262
Calls
4 calls:
278.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
144.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
160.0ms
(/ (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
127.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
120.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
163.0ms
(/ (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
80.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify81.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012545927
150015094

prune801.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ beta (+ alpha (fma 1.0 2.0 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))))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite334.0ms

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:
85.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
107.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
66.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
68.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series421.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
107.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
45.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify69.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05412716
119602543
250012472

prune578.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))
0.2b
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite659.0ms

Algorithm
rewrite-expression-head
Rules
161×times-frac
138×add-exp-log
128×*-un-lft-identity
84×add-sqr-sqrt add-cube-cbrt div-exp
78×add-cbrt-cube
44×cbrt-undiv
27×associate-/l*
24×prod-exp
22×distribute-lft-out
18×associate-/r* associate-/r/
12×cbrt-unprod div-inv
8×rec-exp 1-exp
5×pow1 frac-times associate-*r/ associate-*l/ associate-/l/
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×flip3-+ flip-+
1×flip3-- pow-flip flip-- inv-pow
Counts
4 → 255
Calls
4 calls:
147.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
186.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))
185.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))))
128.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series611.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
236.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))
168.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))))
81.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify84.0ms

Algorithm
egg-herbie
Counts
267 → 267
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011636680
150015564

prune688.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.8b

regimes58.0ms

Accuracy

56.2% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch56.0ms

Steps
ItersRangePoint
8
4.8266542845792594e+173
1.0069133071674746e+178
8.48564295701033e+177

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03523
13723
23723

end0.0ms

sample544.0ms

Algorithm
intervals
Results
307.0ms8000×body80valid
94.0ms8000×pre80true