Details

Time bar (total: 11.1s)

sample23.0ms

Algorithm
intervals
Results
10.0ms264×body80valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12317
23717
35517
47217
58417
610817
717717
832617
969717
10264317
done500117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* z (- b y))
0.0b
(+ y (* z (- b y)))
1.3b
(+ (* x y) (* z (- t a)))
25.9b
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
9×times-frac
8×add-exp-log associate-+r+ add-cbrt-cube add-log-exp
6×pow1 distribute-rgt-in sub-neg distribute-lft-in
5×associate-*r*
4×flip3-+ flip-+
3×associate-*l* associate-/r* associate-/l*
2×+-commutative associate-*r/ sum-log associate-/r/ associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative flip-- cbrt-unprod div-inv distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 87
Calls
4 calls:
10.0ms
(* z (- b y))
3.0ms
(+ y (* z (- b y)))
3.0ms
(+ (* x y) (* z (- t a)))
12.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* z (- b y))
32.0ms
(+ y (* z (- b y)))
42.0ms
(+ (* x y) (* z (- t a)))
318.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify501.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
01461497
13511447
212031327
done50001327

prune298.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 26.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (* z (- b y)))
0.2b
(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
1.3b
(+ (* x y) (* z (- t a)))
26.0b
(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
8×associate-+r+ flip3-+ div-exp flip-+ add-log-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv distribute-rgt-in sub-neg distribute-lft-in
2×+-commutative rec-exp frac-2neg 1-exp clear-num sum-log associate-/l/
1×pow-flip inv-pow
Counts
4 → 145
Calls
4 calls:
3.0ms
(+ y (* z (- b y)))
11.0ms
(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
3.0ms
(+ (* x y) (* z (- t a)))
11.0ms
(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.1s

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ y (* z (- b y)))
791.0ms
(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
45.0ms
(+ (* x y) (* z (- t a)))
274.0ms
(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify646.0ms

Counts
157 → 157
Iterations

Useful iterations: 2 (179.0ms)

IterNodesCost
02164144
15263878
215173553
done50013553

prune382.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 26.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a)))))
0.8b
(+ (+ (* z b) y) (* z (- y)))
1.3b
(+ (* x y) (* z (- t a)))
26.0b
(/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube add-log-exp
8×flip3-+ div-exp flip-+
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv associate-+r+ sum-log distribute-rgt-neg-out
2×+-commutative distribute-rgt-in sub-neg rec-exp frac-2neg distribute-lft-in 1-exp div-sub unsub-neg clear-num associate-/l/
1×associate-+l+ pow-flip inv-pow
Counts
4 → 147
Calls
4 calls:
24.0ms
(/ 1 (/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a)))))
17.0ms
(+ (+ (* z b) y) (* z (- y)))
3.0ms
(+ (* x y) (* z (- t a)))
38.0ms
(/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a))))

series624.0ms

Counts
4 → 12
Calls
4 calls:
455.0ms
(/ 1 (/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a)))))
30.0ms
(+ (+ (* z b) y) (* z (- y)))
42.0ms
(+ (* x y) (* z (- t a)))
97.0ms
(/ (+ (+ (* z b) y) (* z (- y))) (+ (* x y) (* z (- t a))))

simplify729.0ms

Counts
159 → 159
Iterations

Useful iterations: done (719.0ms)

IterNodesCost
02234778
15564332
217433985
done50003980

prune429.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* z b) y)
0.8b
(- (+ (* z b) y) (* z y))
1.3b
(+ (* z (- t a)) (* x y))
25.9b
(/ (+ (* z (- t a)) (* x y)) (- (+ (* z b) y) (* z y)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
13×add-log-exp
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 associate-+l+
3×sub-neg flip3-+ associate-/r* sum-log flip-+ associate-/l*
2×+-commutative distribute-rgt-in flip3-- distribute-lft-in diff-log associate-/r/ flip-- associate-/l/
1×cbrt-undiv frac-2neg div-exp associate--l+ clear-num div-inv
Counts
4 → 71
Calls
4 calls:
3.0ms
(+ (* z b) y)
22.0ms
(- (+ (* z b) y) (* z y))
5.0ms
(+ (* z (- t a)) (* x y))
31.0ms
(/ (+ (* z (- t a)) (* x y)) (- (+ (* z b) y) (* z y)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (* z b) y)
26.0ms
(- (+ (* z b) y) (* z y))
45.0ms
(+ (* z (- t a)) (* x y))
257.0ms
(/ (+ (* z (- t a)) (* x y)) (- (+ (* z b) y) (* z y)))

simplify1.6s

Counts
83 → 83
Iterations

Useful iterations: 3 (487.0ms)

IterNodesCost
01251541
13381503
211041383
346331259
done50001259

prune456.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.5b

regimes550.0ms

Accuracy

25.1% (9.5b remaining)

Error of 20.4b against oracle of 10.9b and baseline of 23.6b

bsearch102.0ms

Steps
ItersRangePoint
9
1.5247250177203267e+35
7.86294764107312e+43
7.736950116967238e+43
8
-1.4335373150418553e+75
-4.5705223523792306e+70
-7.710255796225628e+72

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02643
13835
done3835

end0.0ms

sample639.0ms

Algorithm
intervals
Results
349.0ms8392×body80valid