Details

Time bar (total: 20.1s)

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.1b

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))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite290.0ms

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:
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
40.0ms
(/ (/ (/ (+ (+ (+ 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))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series367.0ms

Counts
3 → 9
Calls
3 calls:
141.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
149.0ms
(/ (/ (/ (+ (+ (+ 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))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify132.0ms

Algorithm
egg-herbie
Counts
465 → 465
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0145512992
1500112037

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.9b

localize13.0ms

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
(/ (* 1 (/ (/ (+ (+ (+ 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))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
118×times-frac
101×*-un-lft-identity
65×add-sqr-sqrt add-cube-cbrt
33×add-exp-log
24×add-cbrt-cube
23×associate-/l*
18×distribute-lft-out
17×div-exp
14×associate-/r/
11×cbrt-undiv
10×associate-/r*
8×flip3-+ flip-+
7×div-inv
6×prod-exp
4×associate-/l/
3×pow1 expm1-log1p-u frac-2neg 1-exp clear-num cbrt-unprod log1p-expm1-u add-log-exp
1×associate-*r/
Counts
3 → 166
Calls
3 calls:
26.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
30.0ms
(/ (* 1 (/ (/ (+ (+ (+ 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)))

series374.0ms

Counts
3 → 9
Calls
3 calls:
143.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
149.0ms
(/ (* 1 (/ (/ (+ (+ (+ 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))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify104.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07773369
138582872
250012855

prune450.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
0.0b
(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
0.6b
(/ 1 (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
377×*-un-lft-identity
310×times-frac
147×add-sqr-sqrt
138×add-cube-cbrt
136×distribute-lft-out
85×associate-*l*
54×add-exp-log
34×add-cbrt-cube
24×div-exp
20×associate-/r*
15×div-inv
14×cbrt-undiv
12×prod-exp associate-/l*
9×pow1
6×cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg associate-*r* clear-num associate-/r/ unswap-sqr
2×pow-flip flip3-+ pow-prod-down associate-*l/ flip-+ fma-udef
1×distribute-rgt-in distribute-lft-in *-commutative inv-pow
Counts
4 → 305
Calls
4 calls:
16.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
30.0ms
(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
20.0ms
(/ 1 (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
11.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
235.0ms
(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
160.0ms
(/ 1 (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
83.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify146.0ms

Algorithm
egg-herbie
Counts
317 → 317
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
08925409
144414944
250014942

prune709.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite710.0ms

Algorithm
rewrite-expression-head
Rules
10146×times-frac
6530×*-un-lft-identity
5526×cbrt-prod
3740×add-sqr-sqrt add-cube-cbrt
1848×sqrt-prod
1395×distribute-lft-out
643×associate-/r/
333×div-inv
313×flip3-+ flip-+
161×associate-/r*
33×associate-/l*
23×cbrt-div
15×add-exp-log
12×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 → 3494
Calls
4 calls:
120.0ms
(/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
14.0ms
(/ (+ (+ (+ 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)))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series735.0ms

Counts
4 → 12
Calls
4 calls:
497.0ms
(/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (/ (+ (+ (+ 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)))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.5s

Algorithm
egg-herbie
Counts
3506 → 3506
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
05001178523

prune11.9s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes60.0ms

Accuracy

73.5% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 3.9b

bsearch74.0ms

Steps
ItersRangePoint
10
2.3269465937382384e+161
1.186466747649906e+173
2.3696559474422673e+161

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04026
14226
24226

end0.0ms

sample556.0ms

Algorithm
intervals
Results
309.0ms8000×body80valid
97.0ms8000×pre80true