Details

Time bar (total: 8.8s)

sample28.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms256×pre80true

simplify84.0ms

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)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.9b

Counts
2 → 2

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))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite116.0ms

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)))
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)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
190.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
159.0ms
(/ (/ (/ (+ (+ (+ 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))
84.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify142.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0153413079
1500112129

prune1.0s

Filtered
487 candidates to 297 candidates (61.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New4789487
Fresh101
Picked101
Done000
Total4809489

Merged error: 0.7b

Counts
489 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
0.1b
(/ (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
81×times-frac
64×add-exp-log
50×add-sqr-sqrt
45×add-cube-cbrt
34×add-cbrt-cube
30×div-exp distribute-lft-out
21×associate-*l*
14×cbrt-undiv prod-exp associate-/l*
12×associate-/r/
10×associate-/r*
9×pow1 div-inv
7×associate-*l/
6×rec-exp 1-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ associate-*r* clear-num flip-+
2×pow-flip pow-prod-down fma-udef unswap-sqr
1×distribute-rgt-in distribute-lft-in *-commutative associate-/l/ inv-pow
Counts
4 → 191
Calls
4 calls:
14.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
11.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
19.0ms
(/ (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
7.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))

series569.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
151.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
163.0ms
(/ (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
99.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))

simplify106.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07082970
138262595
250022564

prune398.0ms

Filtered
203 candidates to 116 candidates (57.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1985203
Fresh448
Picked101
Done000
Total2039212

Merged error: 0.0b

Counts
212 → 9

localize17.0ms

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)))) (/ (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)))))
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))))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite469.0ms

Algorithm
rewrite-expression-head
Rules
1777×times-frac
1545×*-un-lft-identity
761×add-sqr-sqrt
747×sqrt-prod
678×add-cube-cbrt
497×distribute-lft-out
321×associate-*r*
104×associate-/r/
71×associate-/l*
63×associate-*l*
54×flip3-+ flip-+
52×div-inv
20×unswap-sqr
15×add-exp-log add-cbrt-cube
11×associate-/r*
6×pow1
5×associate-/l/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg sqrt-div clear-num
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 896
Calls
4 calls:
304.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (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)))))
39.0ms
(/ (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))))
15.0ms
(/ (+ (+ (+ 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)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (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)))))
138.0ms
(/ (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))))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify287.0ms

Algorithm
egg-herbie
Counts
908 → 908
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0198828172
1500127048

prune2.5s

Filtered
908 candidates to 506 candidates (55.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New9080908
Fresh088
Picked011
Done000
Total9089917

Merged error: 0.0b

Counts
917 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (fma 1.0 2.0 (+ alpha beta)))
0.0b
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)))
0.2b
(/ 1 (* (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (fma 1.0 2.0 (+ alpha beta))))
3.6b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
67×*-un-lft-identity
54×add-exp-log
34×times-frac add-cbrt-cube
32×add-sqr-sqrt
27×add-cube-cbrt
24×associate-*r* distribute-lft-out
22×prod-exp
17×pow1
16×associate-*l/
14×div-exp
12×cbrt-unprod
9×associate-/r/
8×cbrt-undiv flip3-+ flip-+
7×pow-prod-down
6×frac-times associate-*l* associate-/r* associate-/l*
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×pow-flip associate-*r/ div-inv
2×frac-2neg clear-num *-commutative fma-udef unswap-sqr
1×distribute-rgt-in distribute-lft-in inv-pow
Counts
4 → 160
Calls
4 calls:
16.0ms
(* (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (fma 1.0 2.0 (+ alpha beta)))
16.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)))
20.0ms
(/ 1 (* (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (fma 1.0 2.0 (+ alpha beta))))
7.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))

series671.0ms

Counts
4 → 12
Calls
4 calls:
253.0ms
(* (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (fma 1.0 2.0 (+ alpha beta)))
147.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)))
169.0ms
(/ 1 (* (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (fma 1.0 2.0 (+ alpha beta))))
102.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))

simplify111.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06632318
136331978
250031969

prune373.0ms

Filtered
172 candidates to 106 candidates (61.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1711172
Fresh167
Picked101
Done011
Total1738181

Merged error: 0.0b

Counts
181 → 8

regimes84.0ms

Accuracy

67% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 3.8b

bsearch73.0ms

Steps
ItersRangePoint
9
8.266191914910931e+164
5.305280681558894e+172
8.382811420001222e+164

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04439
14439

end0.0ms

sample667.0ms

Algorithm
intervals
Results
376.0ms8000×body80valid
130.0ms8000×pre80true