Details

Time bar (total: 9.4s)

sample41.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
5.0ms256×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: 2.3b

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))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite603.0ms

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:
16.0ms
(+ (+ alpha beta) (* beta alpha))
166.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
248.0ms
(/ (/ (/ (+ (+ (+ 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))
140.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
143.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
155.0ms
(/ (/ (/ (+ (+ (+ 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))
81.0ms
(/ (+ (+ (+ 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

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.1b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite682.0ms

Algorithm
rewrite-expression-head
Rules
407×times-frac
391×*-un-lft-identity
293×sqrt-prod
222×add-sqr-sqrt
198×add-cube-cbrt
110×associate-*l*
107×distribute-lft-out
31×associate-/r/
29×associate-/l*
19×flip3-+ flip-+
16×div-inv
15×add-exp-log add-cbrt-cube
12×associate-/r*
8×sqrt-div unswap-sqr
6×pow1 associate-*r*
5×associate-/l/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ prod-exp cbrt-unprod
1×sqrt-undiv pow-prod-down associate-*l/ *-commutative
Counts
4 → 389
Calls
4 calls:
246.0ms
(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
134.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
138.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
139.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
200.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
81.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify151.0ms

Algorithm
egg-herbie
Counts
401 → 401
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
09958715
135748229
250028154

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b
(/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
0.7b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite608.0ms

Algorithm
rewrite-expression-head
Rules
242×times-frac
190×*-un-lft-identity
152×add-sqr-sqrt
124×add-cube-cbrt
58×associate-*r*
54×add-exp-log
34×add-cbrt-cube
32×distribute-lft-out
26×div-exp
25×associate-/l*
16×associate-*l* associate-/r/
14×cbrt-undiv
12×div-inv
10×prod-exp associate-/r*
9×flip3-+ flip-+
8×unswap-sqr
7×pow1
6×cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/l/
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 280
Calls
4 calls:
62.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
99.0ms
(/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
305.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
128.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
70.0ms
(/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
160.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
84.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify69.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010824573
150024048

prune764.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize16.0ms

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)))
0.8b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite314.0ms

Algorithm
rewrite-expression-head
Rules
59×*-un-lft-identity
52×times-frac
34×add-sqr-sqrt
32×add-cube-cbrt
20×add-exp-log add-cbrt-cube associate-/l*
14×distribute-lft-out
9×add-log-exp
7×cbrt-undiv div-exp
6×pow1
5×associate-*l*
4×expm1-log1p-u fma-def flip3-+ associate-*l/ associate-/r* flip-+ log1p-expm1-u div-inv
3×associate-*r* prod-exp sum-log cbrt-unprod associate-/l/
2×frac-2neg clear-num associate-/r/ fma-udef
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 136
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
29.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
138.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
127.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ (+ alpha beta) (* beta alpha))
39.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
170.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
84.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify84.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06121863
130061619
250011609

prune420.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.5b

regimes74.0ms

Accuracy

52.3% (1.3b remaining)

Error of 2.5b against oracle of 1.2b and baseline of 3.9b

bsearch71.0ms

Steps
ItersRangePoint
7
3.1516007484118213e+187
5.144035700259534e+189
4.519845577804869e+187

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04644
14644

end0.0ms

sample1.1s

Algorithm
intervals
Results
766.0ms8000×body80valid
147.0ms8000×pre80true