Details

Time bar (total: 22.3s)

sample33.0ms

Algorithm
intervals
Results
14.0ms264×body80valid

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12416
24315
37515
411215
514815
618115
725715
841915
972815
10152515
11409615
done500015

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (* z (- b y)))
0.0b
(* z (- b y))
0.2b
(+ (* x y) (* z (- t a)))
22.6b
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
54×prod-diff
53×*-un-lft-identity
51×add-cube-cbrt
44×associate-+r+
33×distribute-rgt-in distribute-lft-in
9×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×pow1 sub-neg
5×associate-*r*
4×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u
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 → 153
Calls
4 calls:
15.0ms
(+ y (* z (- b y)))
33.0ms
(* z (- b y))
24.0ms
(+ (* x y) (* z (- t a)))
47.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series568.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ y (* z (- b y)))
53.0ms
(* z (- b y))
56.0ms
(+ (* x y) (* z (- t a)))
427.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify1.1s

Counts
165 → 165
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02772673
15912249
215331865
done50001793

prune607.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (- b y) z y)
0.2b
(+ (* x y) (* z (- t a)))
1.0b
(/ 1 (fma (- b y) z y))
22.1b
(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
33×*-un-lft-identity
32×add-cube-cbrt
22×associate-+r+
20×times-frac
18×prod-diff
17×add-exp-log
13×associate-*r*
11×distribute-rgt-in distribute-lft-in add-cbrt-cube
7×pow1
6×add-log-exp
4×expm1-log1p-u div-exp prod-exp log1p-expm1-u
3×flip3-+ associate-*l* associate-/r* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times sub-neg rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×+-commutative pow-flip fma-def frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative fma-udef inv-pow
Counts
4 → 121
Calls
4 calls:
0.0ms
(fma (- b y) z y)
18.0ms
(+ (* x y) (* z (- t a)))
5.0ms
(/ 1 (fma (- b y) z y))
31.0ms
(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

series706.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(fma (- b y) z y)
56.0ms
(+ (* x y) (* z (- t a)))
109.0ms
(/ 1 (fma (- b y) z y))
508.0ms
(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

simplify1.2s

Counts
133 → 133
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01942148
14421836
212081606
done50011582

prune541.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (- b y) z y)
0.3b
(fma x y (* z (- t a)))
0.6b
(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
22.5b
(/ (fma (- b y) z y) (fma x y (* z (- t a))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×add-exp-log
16×associate-/r*
11×add-cbrt-cube
8×div-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp clear-num fma-udef
1×pow-flip associate-/r/ inv-pow
Counts
4 → 127
Calls
4 calls:
0.0ms
(fma (- b y) z y)
0.0ms
(fma x y (* z (- t a)))
12.0ms
(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
6.0ms
(/ (fma (- b y) z y) (fma x y (* z (- t a))))

series1.9s

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma (- b y) z y)
55.0ms
(fma x y (* z (- t a)))
1.6s
(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
232.0ms
(/ (fma (- b y) z y) (fma x y (* z (- t a))))

simplify2.1s

Counts
139 → 139
Iterations

Useful iterations: 3 (828.0ms)

IterNodesCost
01783291
13513072
27212775
325092757
done50022757

prune499.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma x y (* z (- t a)))
0.6b
(/ 1 (* (fma (- b y) z y) (/ 1 (fma x y (* z (- t a))))))
0.8b
(/ 1 (fma x y (* z (- t a))))
21.8b
(* (fma (- b y) z y) (/ 1 (fma x y (* z (- t a)))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log
29×add-sqr-sqrt
23×*-un-lft-identity times-frac
22×add-cube-cbrt
20×div-exp add-cbrt-cube
16×prod-exp
13×associate-*r*
10×pow1 rec-exp 1-exp
6×cbrt-undiv associate-/l*
4×expm1-log1p-u associate-/r* cbrt-unprod log1p-expm1-u add-log-exp
3×pow-flip associate-*l* div-inv unswap-sqr
2×frac-2neg associate-*r/ pow-prod-down clear-num associate-/r/ un-div-inv inv-pow
1×*-commutative fma-udef
Counts
4 → 123
Calls
4 calls:
0.0ms
(fma x y (* z (- t a)))
19.0ms
(/ 1 (* (fma (- b y) z y) (/ 1 (fma x y (* z (- t a))))))
6.0ms
(/ 1 (fma x y (* z (- t a))))
27.0ms
(* (fma (- b y) z y) (/ 1 (fma x y (* z (- t a)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
68.0ms
(fma x y (* z (- t a)))
1.5s
(/ 1 (* (fma (- b y) z y) (/ 1 (fma x y (* z (- t a))))))
110.0ms
(/ 1 (fma x y (* z (- t a))))
218.0ms
(* (fma (- b y) z y) (/ 1 (fma x y (* z (- t a)))))

simplify2.9s

Counts
135 → 135
Iterations

Useful iterations: 2 (141.0ms)

IterNodesCost
01472456
13032164
27581824
325981824
done50021824

prune421.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.6b

regimes526.0ms

Accuracy

33.7% (8.2b remaining)

Error of 18.8b against oracle of 10.7b and baseline of 23.0b

bsearch144.0ms

Steps
ItersRangePoint
7
1.2097950679130598e+120
2.8096875911191325e+121
4.516505167907681e+120
9
-1.0954634436734111e+126
-2.1249283703095122e+118
-5.05944825619139e+125

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02440
13334
done3334

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.1s8422×body80valid