Details

Time bar (total: 6.8s)

sample25.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify81.0ms

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: 3.1b

Counts
2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
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))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite110.0ms

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
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 476
Calls
4 calls:
12.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
36.0ms
(/ (/ (/ (+ (+ (+ 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)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
134.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
144.0ms
(/ (/ (/ (+ (+ (+ 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))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify144.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0151312983
1500212137

prune959.0ms

Filtered
488 candidates to 299 candidates (61.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4808488
Fresh101
Picked101
Done000
Total4828490

Merged error: 0.9b

Counts
490 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
0.1b
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite57.0ms

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:
10.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
11.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
19.0ms
(/ (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 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)) (+ beta (+ alpha (fma alpha beta 1.0))))

series533.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
145.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
149.0ms
(/ (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
96.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify105.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07192968
138412593
250012562

prune380.0ms

Filtered
203 candidates to 117 candidates (57.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2021203
Fresh257
Picked011
Done000
Total2047211

Merged error: 0.0b

Counts
211 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
69×times-frac
47×add-sqr-sqrt
43×add-cube-cbrt
40×sqrt-prod
29×associate-/l*
18×flip3-+ flip-+
17×distribute-lft-out
16×associate-/r/
15×add-exp-log add-cbrt-cube
13×sqrt-div
8×frac-times
7×associate-/r*
6×pow1 associate-*r*
5×associate-*l* div-inv associate-/l/
4×cbrt-undiv expm1-log1p-u associate-*r/ div-exp associate-*l/ log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×prod-exp cbrt-unprod unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 176
Calls
4 calls:
13.0ms
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms
(/ (+ (+ (+ 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)))
31.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

series354.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
70.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
74.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
129.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

simplify98.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06763073
130172821
250012801

prune801.0ms

Filtered
188 candidates to 145 candidates (77.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1880188
Fresh055
Picked011
Done011
Total1887195

Merged error: 0.0b

Counts
195 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
1.6b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.3b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
756×times-frac
594×*-un-lft-identity
419×sqrt-prod
372×add-sqr-sqrt add-cube-cbrt
111×distribute-lft-out
61×associate-/l*
40×sqrt-div associate-/r/
26×associate-/r*
24×add-exp-log
21×flip3-+ flip-+
20×div-inv
18×add-cbrt-cube
12×div-exp
8×cbrt-undiv
6×pow1
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
3×pow-flip
2×rec-exp 1-exp
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 587
Calls
4 calls:
8.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
24.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
30.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series412.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
101.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
157.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
93.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify157.0ms

Algorithm
egg-herbie
Counts
599 → 599
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0136913739
1500112934

prune1.1s

Filtered
599 candidates to 257 candidates (42.9%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New5990599
Fresh044
Picked011
Done022
Total5997606

Merged error: 0.0b

Counts
606 → 7

regimes77.0ms

Accuracy

67.7% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.5b

bsearch70.0ms

Steps
ItersRangePoint
9
5.975337806150348e+154
3.290857389681513e+162
3.2003140598161636e+156

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03825
13825

end0.0ms

sample634.0ms

Algorithm
intervals
Results
360.0ms8000×body80valid
127.0ms8000×pre80true