Details

Time bar (total: 19.7s)

sample26.0ms

Algorithm
intervals
Results
8.0ms250×body80valid
2.0ms14×body640valid
1.0ms15×body320valid
1.0ms9×body160valid
0.0ms3×body1280valid
0.0ms1×body2560valid

simplify6.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01113
12313
24512
312112
429612
571312
6145712
7275712
8449312
done500012

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
11.2b
(fma (/ (- t x) (- a z)) (- y z) x)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
12.0ms
(/ (- t x) (- a z))
0.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

series136.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(/ (- t x) (- a z))
84.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.8s

Counts
70 → 70
Iterations

Useful iterations: 4 (971.0ms)

IterNodesCost
0118918
1269890
2628838
31593834
44635828
done5000828

prune227.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- a z))
0.3b
(* (- t x) (/ 1 (- a z)))
11.1b
(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×*-un-lft-identity
32×times-frac
23×add-cube-cbrt
21×associate-*r*
16×add-exp-log
10×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-*l* associate-/r*
4×flip3-- div-exp prod-exp associate-/r/ flip--
3×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative fma-udef inv-pow
Counts
3 → 105
Calls
3 calls:
5.0ms
(/ 1 (- a z))
24.0ms
(* (- t x) (/ 1 (- a z)))
0.0ms
(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series172.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ 1 (- a z))
52.0ms
(* (- t x) (/ 1 (- a z)))
84.0ms
(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify2.1s

Counts
114 → 114
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01551285
13511052
2947948
33111944
done5000943

prune272.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ t (- a z))
0.0b
(/ x (- a z))
0.0b
(- (/ t (- a z)) (/ x (- a z)))
11.2b
(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
713×*-un-lft-identity
703×add-sqr-sqrt
693×times-frac
441×prod-diff
413×add-cube-cbrt
149×distribute-lft-out--
143×difference-of-squares
94×associate-/r/
48×flip3-- flip--
47×div-inv
21×fma-neg
10×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×distribute-rgt-out--
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg diff-log frac-sub fma-udef sub-div
Counts
4 → 581
Calls
4 calls:
5.0ms
(/ t (- a z))
6.0ms
(/ x (- a z))
73.0ms
(- (/ t (- a z)) (/ x (- a z)))
0.0ms
(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

series269.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ t (- a z))
28.0ms
(/ x (- a z))
109.0ms
(- (/ t (- a z)) (/ x (- a z)))
104.0ms
(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

simplify1.1s

Counts
593 → 593
Iterations

Useful iterations: done (1.0s)

IterNodesCost
057428436
1119625539
2279119581
done500019476

prune1.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ t (- a z))
0.0b
(- (/ t (- a z)) (/ x (- a z)))
3.7b
(* (- (/ t (- a z)) (/ x (- a z))) (- y z))
4.3b
(+ (* (- (/ t (- a z)) (/ x (- a z))) (- y z)) x)

rewrite408.0ms

Algorithm
rewrite-expression-head
Rules
751×*-un-lft-identity
733×add-sqr-sqrt
696×times-frac
477×prod-diff
431×add-cube-cbrt
158×distribute-lft-out--
146×difference-of-squares
96×associate-/r/
57×flip3-- flip--
48×div-inv
22×distribute-rgt-in associate-+l+ distribute-lft-in
21×fma-neg
18×associate-*l*
8×add-exp-log frac-times add-cbrt-cube add-log-exp
6×pow1 distribute-rgt-out--
5×sub-neg associate-*r* associate-/r*
4×expm1-log1p-u associate-*l/ frac-sub log1p-expm1-u sub-div
3×associate-/l*
2×associate-*r/
1×cbrt-undiv +-commutative fma-def frac-2neg flip3-+ diff-log div-exp pow-prod-down prod-exp clear-num sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 641
Calls
4 calls:
6.0ms
(/ t (- a z))
71.0ms
(- (/ t (- a z)) (/ x (- a z)))
185.0ms
(* (- (/ t (- a z)) (/ x (- a z))) (- y z))
84.0ms
(+ (* (- (/ t (- a z)) (/ x (- a z))) (- y z)) x)

series543.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ t (- a z))
105.0ms
(- (/ t (- a z)) (/ x (- a z)))
252.0ms
(* (- (/ t (- a z)) (/ x (- a z))) (- y z))
155.0ms
(+ (* (- (/ t (- a z)) (/ x (- a z))) (- y z)) x)

simplify1.7s

Counts
653 → 653
Iterations

Useful iterations: done (1.7s)

IterNodesCost
069630832
1150427597
2413321481
done500021340

prune1.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 6.2b

regimes362.0ms

Accuracy

14.9% (6.9b remaining)

Error of 13.4b against oracle of 6.5b and baseline of 14.6b

bsearch57.0ms

Steps
ItersRangePoint
4
5.581274792083229e+225
1.1004066369351343e+226
6.501016910978108e+225
6
-4.356485418338831e+232
-1.0295582727544921e+232
-3.2582793557416086e+232

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01824
12424
done2424

end0.0ms

sample719.0ms

Algorithm
intervals
Results
268.0ms7794×body80valid
60.0ms460×body640valid
42.0ms435×body320valid
40.0ms255×body1280valid
18.0ms280×body160valid
3.0ms14×body2560valid