Details

Time bar (total: 1.4m)

sample22.0ms

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

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.9b

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))
1.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite123.0ms

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)))
43.0ms
(/ (/ (/ (+ (+ (+ 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))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
144.0ms
(/ (/ (+ (+ (+ 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))
73.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify137.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0153413079
1500112129

prune1.1s

Filtered
487 candidates to 297 candidates (61.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.4b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.7b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
1.7b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
80×sqrt-prod
76×*-un-lft-identity
74×add-sqr-sqrt
67×times-frac
52×add-cube-cbrt
27×associate-*l*
14×sqrt-div
12×distribute-lft-out
11×add-exp-log add-cbrt-cube
8×pow1
7×flip3-+ flip-+ associate-/l*
6×associate-*r* associate-/r* unswap-sqr
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ div-exp prod-exp cbrt-unprod hypot-def div-inv associate-/l/
1×sqrt-undiv frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 171
Calls
4 calls:
25.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
16.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
8.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series665.0ms

Counts
4 → 12
Calls
4 calls:
466.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
103.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
50.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify218.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05702661
122982425
250012368

prune597.0ms

Filtered
183 candidates to 121 candidates (66.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
0.1b
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
1.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
1.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite5.5s

Algorithm
rewrite-expression-head
Rules
98889×times-frac
64792×*-un-lft-identity
38820×sqrt-prod
32650×add-sqr-sqrt add-cube-cbrt
18119×distribute-lft-out
5246×associate-/r/
2656×div-inv
2593×flip3-+ flip-+
389×associate-/r*
76×associate-/l*
66×sqrt-div
15×add-exp-log add-cbrt-cube
7×associate-/l/
6×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
Counts
4 → 21035
Calls
4 calls:
597.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
40.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
18.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series590.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
278.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
74.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify12.5s

Algorithm
egg-herbie
Counts
21047 → 21047
Iterations

Useful iterations: 0 (175.0ms)

IterNodesCost
0166951396902

prune56.6s

Filtered
21047 candidates to 7904 candidates (37.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.5b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.0b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
206×*-un-lft-identity
136×add-sqr-sqrt add-cube-cbrt
75×sqrt-prod
41×associate-/l*
35×distribute-lft-out
18×associate-/r*
17×add-exp-log
16×associate-/r/
15×add-cbrt-cube
12×sqrt-div
10×flip3-+ flip-+
8×div-inv
7×div-exp
6×pow1 cbrt-undiv
5×associate-/l/
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×pow-flip
1×rec-exp sqrt-pow1 pow1/2 1-exp inv-pow
Counts
4 → 280
Calls
4 calls:
24.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
8.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
21.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
16.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series448.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
70.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
97.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify123.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
09245167
141104735
250014724

prune1.2s

Filtered
292 candidates to 184 candidates (63.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

regimes81.0ms

Accuracy

0% (2.3b remaining)

Error of 3.5b against oracle of 1.1b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02729
12729

end0.0ms

sample528.0ms

Algorithm
intervals
Results
290.0ms8000×body80valid
99.0ms8000×pre80true