Details

Time bar (total: 23.1s)

sample22.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify86.0ms

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: 5.1b

localize16.0ms

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)))

rewrite600.0ms

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:
169.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
253.0ms
(/ (/ (/ (+ (+ (+ 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))
144.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series382.0ms

Counts
3 → 9
Calls
3 calls:
146.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
156.0ms
(/ (/ (/ (+ (+ (+ 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))
80.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify131.0ms

Algorithm
egg-herbie
Counts
465 → 465
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0145512992
1500112037

prune1.3s

Filtered
465 candidates to 281 candidates (60.4%)
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
(/ (pow (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) 1) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite763.0ms

Algorithm
rewrite-expression-head
Rules
820×times-frac
600×*-un-lft-identity
348×add-sqr-sqrt add-cube-cbrt
300×unpow-prod-down
126×distribute-lft-out
86×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
22×add-exp-log
12×div-exp add-cbrt-cube
10×associate-/r*
5×cbrt-undiv sqr-pow
3×pow1 expm1-log1p-u frac-2neg pow-exp clear-num log1p-expm1-u associate-/l/ add-log-exp
1×pow-to-exp
Counts
3 → 475
Calls
3 calls:
171.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
409.0ms
(/ (pow (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) 1) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
144.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series370.0ms

Counts
3 → 9
Calls
3 calls:
139.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms
(/ (pow (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) 1) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
80.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify146.0ms

Algorithm
egg-herbie
Counts
484 → 484
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0142213959
1500213419

prune1.2s

Filtered
484 candidates to 284 candidates (58.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.9b

localize17.0ms

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 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)))

rewrite471.0ms

Algorithm
rewrite-expression-head
Rules
389×*-un-lft-identity
338×times-frac
159×add-sqr-sqrt
150×add-cube-cbrt
136×distribute-lft-out
114×add-exp-log
85×associate-*l*
72×div-exp
52×add-cbrt-cube
25×cbrt-undiv
24×prod-exp
22×associate-/l*
20×1-exp associate-/r*
17×div-inv
9×cbrt-unprod
8×rec-exp
6×pow1
5×associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* clear-num associate-/r/ unswap-sqr
2×flip3-+ associate-*l/ flip-+ fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative
Counts
4 → 343
Calls
4 calls:
89.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
178.0ms
(* (/ (+ 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)))
50.0ms
(/ (/ 1 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))))
129.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series612.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
239.0ms
(* (/ (+ 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)))
164.0ms
(/ (/ 1 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))))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify89.0ms

Algorithm
egg-herbie
Counts
355 → 355
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011456197
150015584

prune785.0ms

Filtered
355 candidates to 187 candidates (52.7%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize20.0ms

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)))

rewrite1.3s

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:
341.0ms
(/ (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))))))
139.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
141.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
145.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series753.0ms

Counts
4 → 12
Calls
4 calls:
507.0ms
(/ (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))))))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
80.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
83.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.5s

Algorithm
egg-herbie
Counts
3506 → 3506
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
05001178523

prune12.0s

Filtered
3506 candidates to 1727 candidates (49.3%)
Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes70.0ms

Accuracy

73.4% (1.0b remaining)

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

bsearch77.0ms

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
14026

end0.0ms

sample536.0ms

Algorithm
intervals
Results
301.0ms8000×body80valid
93.0ms8000×pre80true