Details

Time bar (total: 7.0m)

sample28.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
3.0ms256×pre80true

simplify77.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune2.0ms

Pruning

1 alts after pruning (1 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)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×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 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
27.0ms
(+ (+ alpha beta) (* beta alpha))
330.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
477.0ms
(/ (/ (/ (+ (+ (+ 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))
281.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ alpha beta) (* beta alpha))
129.0ms
(/ (/ (+ (+ (+ 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))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify138.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0151213008
1500112540

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.5b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
12132×times-frac
7340×*-un-lft-identity
4744×add-sqr-sqrt add-cube-cbrt
3270×sqrt-prod
1298×distribute-lft-out
784×associate-/l*
298×associate-/r/
284×sqrt-div
150×flip3-+ flip-+
149×div-inv
34×add-exp-log add-cbrt-cube
20×cbrt-undiv div-exp
19×associate-/r*
5×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
Counts
4 → 3894
Calls
4 calls:
430.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
691.0ms
(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
346.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
286.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series440.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
140.0ms
(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ 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) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
93.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify1.3s

Algorithm
egg-herbie
Counts
3906 → 3906
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
05001163477

prune9.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (+ (+ alpha beta) (* 2.0 1.0)))
2.7b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
14×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt cbrt-div
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
3×distribute-lft-out
Counts
4 → 55
Calls
4 calls:
15.0ms
(cbrt (+ (+ alpha beta) (* 2.0 1.0)))
59.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
59.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
60.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series266.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(cbrt (+ (+ alpha beta) (* 2.0 1.0)))
55.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
56.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify97.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0341762
1982714
24134696
35002696

prune460.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ (/ (/ (/ 1 (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (* (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
1.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
1.3b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
1.4b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite5.5m

Algorithm
rewrite-expression-head
Rules
89256×times-frac
51036×sqrt-prod
43897×add-sqr-sqrt
43077×*-un-lft-identity
29107×add-cube-cbrt
16176×associate-*r*
13726×cbrt-prod
6655×distribute-lft-out
2614×sqrt-div
1938×associate-*l*
1925×unswap-sqr
1458×associate-/r/
814×flip3-+ flip-+
604×cbrt-div
603×div-inv
430×associate-/l*
405×add-exp-log
275×div-exp
217×add-cbrt-cube
169×frac-times
165×cbrt-undiv
85×associate-*r/ associate-*l/
75×prod-exp
45×cbrt-unprod
24×associate-/r*
10×rec-exp 1-exp
6×pow1
4×associate-/l/ add-log-exp
3×frac-2neg clear-num
1×pow-prod-down *-commutative
Counts
4 → 23365
Calls
4 calls:
5.4m
(* (/ (/ (/ (/ 1 (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (* (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
345.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
277.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
510.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (/ (/ (/ (/ 1 (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (* (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
202.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
92.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
1.2s
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (cbrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify11.8s

Algorithm
egg-herbie
Counts
23377 → 23377
Iterations

Useful iterations: 0 (133.0ms)

IterNodesCost
0147661474998

prune1.0m

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.5b

regimes105.0ms

Accuracy

45.4% (1.5b remaining)

Error of 2.6b against oracle of 1.0b and baseline of 3.9b

bsearch69.0ms

Steps
ItersRangePoint
7
4.065080596138508e+126
7.393131719366263e+127
3.549858114861534e+127

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06172
16172

end0.0ms

sample526.0ms

Algorithm
intervals
Results
269.0ms8000×body80valid
84.0ms8000×pre80true