Details

Time bar (total: 7.8s)

sample24.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify84.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03310
17910
221010
348310
491010
5151610
6281810
7500110

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 25.2b

Counts
2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ t y) a)
2.3b
(+ (* (+ x y) z) (* (+ t y) a))
2.4b
(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
23.6b
(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
1050×*-un-lft-identity
500×distribute-lft-out
450×associate-*l*
153×add-sqr-sqrt
144×prod-diff
140×distribute-lft-out--
125×times-frac
90×add-cube-cbrt
42×associate-*r*
25×associate-/l*
21×unswap-sqr
14×*-commutative difference-of-squares
13×fma-def
12×fma-neg
11×add-log-exp
10×associate-*l/
8×add-exp-log add-cbrt-cube
7×flip3-+ flip-+
6×pow1
5×associate-/r*
4×expm1-log1p-u frac-add log1p-expm1-u
2×+-commutative flip3-- diff-log associate--l+ sum-log associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg div-sub div-exp pow-prod-down prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 431
Calls
4 calls:
6.0ms
(* (+ t y) a)
20.0ms
(+ (* (+ x y) z) (* (+ t y) a))
36.0ms
(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
48.0ms
(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series743.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (+ t y) a)
46.0ms
(+ (* (+ x y) z) (* (+ t y) a))
96.0ms
(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
580.0ms
(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify147.0ms

Algorithm
egg-herbie
Counts
443 → 443
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
07946001
134614672
250014667

prune551.0ms

Filtered
443 candidates to 120 candidates (27.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New43112443
Fresh000
Picked101
Done000
Total43212444

Merged error: 7.7b

Counts
444 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ t y) a)
1.3b
(fma (+ x y) z (* (+ t y) a))
7.8b
(/ (* y b) (+ (+ x t) y))
21.7b
(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
232×*-un-lft-identity
179×times-frac
109×add-sqr-sqrt
95×add-cube-cbrt
82×distribute-lft-out
28×associate-/l*
22×associate-*l*
21×associate-*r*
18×add-exp-log
16×add-cbrt-cube
13×associate-/r*
9×associate-/l/
8×div-inv
7×div-exp *-commutative unswap-sqr
6×pow1
5×cbrt-undiv
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ clear-num flip-+
2×associate-*l/ prod-exp cbrt-unprod
1×1-exp pow-prod-down fma-udef
Counts
4 → 239
Calls
4 calls:
6.0ms
(* (+ t y) a)
1.0ms
(fma (+ x y) z (* (+ t y) a))
15.0ms
(/ (* y b) (+ (+ x t) y))
11.0ms
(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series372.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (+ t y) a)
52.0ms
(fma (+ x y) z (* (+ t y) a))
75.0ms
(/ (* y b) (+ (+ x t) y))
223.0ms
(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify101.0ms

Algorithm
egg-herbie
Counts
251 → 251
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07512431
134822256
250012153

prune620.0ms

Filtered
251 candidates to 135 candidates (53.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2456251
Fresh5611
Picked101
Done000
Total25112263

Merged error: 5.5b

Counts
263 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ t y) a)
1.3b
(fma (+ x y) z (* (+ t y) a))
3.6b
(* b (/ y (+ (+ x t) y)))
21.7b
(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
169×*-un-lft-identity
135×times-frac
83×add-sqr-sqrt
76×add-cube-cbrt
55×distribute-lft-out
24×associate-*r*
20×associate-/l*
18×add-exp-log
16×add-cbrt-cube
13×associate-/r*
11×associate-*r/
9×associate-/l/
8×pow1 div-inv
7×associate-*l*
6×div-exp
4×cbrt-undiv expm1-log1p-u clear-num associate-/r/ log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ prod-exp cbrt-unprod flip-+ unswap-sqr
2×pow-prod-down associate-*l/ un-div-inv *-commutative
1×1-exp fma-udef
Counts
4 → 198
Calls
4 calls:
6.0ms
(* (+ t y) a)
1.0ms
(fma (+ x y) z (* (+ t y) a))
13.0ms
(* b (/ y (+ (+ x t) y)))
11.0ms
(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series337.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (+ t y) a)
52.0ms
(fma (+ x y) z (* (+ t y) a))
43.0ms
(* b (/ y (+ (+ x t) y)))
220.0ms
(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify91.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06791980
130571805
250011702

prune518.0ms

Filtered
210 candidates to 114 candidates (54.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2019210
Fresh9211
Picked011
Done000
Total21012222

Merged error: 4.3b

Counts
222 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

5.7b
(/ (* (cbrt (fma (+ x y) z (* (+ t y) a))) (cbrt (fma (+ x y) z (* (+ t y) a)))) (cbrt (+ (+ x t) y)))
22.5b
(cbrt (fma (+ x y) z (* (+ t y) a)))
22.5b
(cbrt (fma (+ x y) z (* (+ t y) a)))
22.5b
(cbrt (fma (+ x y) z (* (+ t y) a)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
293×cbrt-prod
284×*-un-lft-identity
216×add-sqr-sqrt times-frac
144×add-cube-cbrt
84×distribute-lft-out
54×swap-sqr associate-*r* associate-*l*
36×unswap-sqr
27×associate-/l*
19×add-cbrt-cube
10×cbrt-undiv
9×add-exp-log *-commutative
8×associate-/r* cbrt-unprod
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3
2×cbrt-div div-exp associate-/r/
1×frac-2neg flip3-+ prod-exp clear-num flip-+ div-inv
Counts
4 → 316
Calls
4 calls:
20.0ms
(/ (* (cbrt (fma (+ x y) z (* (+ t y) a))) (cbrt (fma (+ x y) z (* (+ t y) a)))) (cbrt (+ (+ x t) y)))
1.0ms
(cbrt (fma (+ x y) z (* (+ t y) a)))
1.0ms
(cbrt (fma (+ x y) z (* (+ t y) a)))
1.0ms
(cbrt (fma (+ x y) z (* (+ t y) a)))

series1.3s

Counts
4 → 12
Calls
4 calls:
568.0ms
(/ (* (cbrt (fma (+ x y) z (* (+ t y) a))) (cbrt (fma (+ x y) z (* (+ t y) a)))) (cbrt (+ (+ x t) y)))
253.0ms
(cbrt (fma (+ x y) z (* (+ t y) a)))
254.0ms
(cbrt (fma (+ x y) z (* (+ t y) a)))
255.0ms
(cbrt (fma (+ x y) z (* (+ t y) a)))

simplify165.0ms

Algorithm
egg-herbie
Counts
328 → 328
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
08027728
138117217
250016864

prune963.0ms

Filtered
328 candidates to 166 candidates (50.6%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New3271328
Fresh1910
Picked011
Done011
Total32812340

Merged error: 4.3b

Counts
340 → 12

regimes522.0ms

Accuracy

10.1% (18.3b remaining)

Error of 21.5b against oracle of 3.2b and baseline of 23.5b

bsearch241.0ms

Steps
ItersRangePoint
9
1.99290631466662e+53
1.2325178254799744e+61
1.3318142435851507e+60
5
5.7700411409508134e-33
1.451134970391611e-32
8.267036411817142e-33
7
1.457175507265453e-298
1.8755825806786685e-296
4.7765110144586345e-298
7
-5.3828143815109067e-20
-2.9925441002972354e-21
-3.9930459557533415e-21
10
-4.2699642224146114e+189
-4.284391725651818e+179
-1.2734159310100645e+180

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04346
14346

end0.0ms

sample634.0ms

Algorithm
intervals
Results
360.0ms7996×body80valid
0.0ms2×body160valid
0.0ms1×body640valid
0.0ms1×body320valid