Details

Time bar (total: 50.3s)

sample42.0ms

Algorithm
intervals
Results
10.0ms251×body80valid
3.0ms19×body640valid
1.0ms7×body1280valid
1.0ms11×body160valid
1.0ms7×body320valid
1.0ms3×body2560valid

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
011245
120245
243245
3108220
4299220
5788220
61890220
done5000220

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- y x) (- a t))
14.5b
(fma (/ (- y x) (- a t)) (- z t) x)

rewrite21.0ms

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-cbrt-cube add-exp-log
2×expm1-log1p-u pow1 flip3-- associate-/r/ log1p-expm1-u flip-- add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
18.0ms
(/ (- y x) (- a t))
0.0ms
(fma (/ (- y x) (- a t)) (- z t) x)

series224.0ms

Counts
2 → 6
Calls
2 calls:
92.0ms
(/ (- y x) (- a t))
132.0ms
(fma (/ (- y x) (- a t)) (- z t) x)

simplify2.1s

Counts
70 → 70
Iterations

Useful iterations: 3 (737.0ms)

IterNodesCost
011818729
127517805
267317725
3216417675
done500417675

prune465.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y (- a t))
0.0b
(/ x (- a t))
0.3b
(- (/ y (- a t)) (/ x (- a t)))
14.5b
(fma (- (/ y (- a t)) (/ x (- a t))) (- z t) x)

rewrite225.0ms

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-cbrt-cube add-exp-log
6×associate-/l* add-log-exp
4×expm1-log1p-u pow1 log1p-expm1-u
3×distribute-rgt-out--
2×cbrt-undiv clear-num frac-2neg div-exp
1×sub-neg diff-log frac-sub fma-udef sub-div
Counts
4 → 581
Calls
4 calls:
15.0ms
(/ y (- a t))
9.0ms
(/ x (- a t))
118.0ms
(- (/ y (- a t)) (/ x (- a t)))
1.0ms
(fma (- (/ y (- a t)) (/ x (- a t))) (- z t) x)

series431.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ y (- a t))
45.0ms
(/ x (- a t))
165.0ms
(- (/ y (- a t)) (/ x (- a t)))
178.0ms
(fma (- (/ y (- a t)) (/ x (- a t))) (- z t) x)

simplify4.6s

Counts
593 → 593
Iterations

Useful iterations: done (4.4s)

IterNodesCost
0574442169
11285387985
23084346369
done5001307977

prune3.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y (- a t))
0.3b
(* x (/ 1 (- a t)))
0.3b
(- (/ y (- a t)) (* x (/ 1 (- a t))))
14.5b
(fma (- (/ y (- a t)) (* x (/ 1 (- a t)))) (- z t) x)

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
69×*-un-lft-identity
62×times-frac
42×add-cube-cbrt
21×fma-neg associate-*r* prod-diff
15×add-exp-log
13×distribute-lft-out-- difference-of-squares
11×add-cbrt-cube
8×associate-/r/
6×pow1 add-log-exp
5×associate-/r* flip3-- div-inv flip--
4×expm1-log1p-u prod-exp log1p-expm1-u
3×div-exp associate-*l* associate-*r/ un-div-inv associate-/l* unswap-sqr
2×cbrt-undiv frac-sub cbrt-unprod sub-div
1×rec-exp clear-num sub-neg frac-2neg distribute-rgt-out-- diff-log 1-exp pow-prod-down *-commutative fma-udef
Counts
4 → 156
Calls
4 calls:
8.0ms
(/ y (- a t))
28.0ms
(* x (/ 1 (- a t)))
67.0ms
(- (/ y (- a t)) (* x (/ 1 (- a t))))
1.0ms
(fma (- (/ y (- a t)) (* x (/ 1 (- a t)))) (- z t) x)

series461.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ y (- a t))
48.0ms
(* x (/ 1 (- a t)))
178.0ms
(- (/ y (- a t)) (* x (/ 1 (- a t))))
188.0ms
(fma (- (/ y (- a t)) (* x (/ 1 (- a t)))) (- z t) x)

simplify3.3s

Counts
168 → 168
Iterations

Useful iterations: 3 (2.0s)

IterNodesCost
021644889
151539298
2144734996
3473633407
done500033407

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (- a t))
0.3b
(- (/ y (- a t)) (/ x (- a t)))
3.7b
(+ (* (- z t) (- (/ y (- a t)) (/ x (- a t)))) x)
5.3b
(* (- z t) (- (/ y (- a t)) (/ x (- a t))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
3247×*-un-lft-identity
3229×add-sqr-sqrt
3216×times-frac
2205×prod-diff
1919×add-cube-cbrt
886×distribute-rgt-in associate-+l+ distribute-lft-in
662×distribute-lft-out--
650×difference-of-squares
432×associate-/r/
225×flip3-- flip--
216×div-inv
21×fma-neg
18×associate-*r*
8×frac-times add-cbrt-cube add-exp-log add-log-exp
6×pow1 distribute-rgt-out--
5×associate-/r* sub-neg associate-*l*
4×expm1-log1p-u associate-*r/ frac-sub log1p-expm1-u sub-div
3×associate-/l*
2×associate-*l/
1×cbrt-undiv +-commutative clear-num sum-log fma-def frac-2neg flip3-+ diff-log div-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 2369
Calls
4 calls:
17.0ms
(/ x (- a t))
118.0ms
(- (/ y (- a t)) (/ x (- a t)))
276.0ms
(+ (* (- z t) (- (/ y (- a t)) (/ x (- a t)))) x)
388.0ms
(* (- z t) (- (/ y (- a t)) (/ x (- a t))))

series656.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ x (- a t))
160.0ms
(- (/ y (- a t)) (/ x (- a t)))
223.0ms
(+ (* (- z t) (- (/ y (- a t)) (/ x (- a t)))) x)
240.0ms
(* (- z t) (- (/ y (- a t)) (/ x (- a t))))

simplify7.3s

Counts
2381 → 2381
Iterations

Useful iterations: done (6.5s)

IterNodesCost
013601849289
130121612697
done50001487143

prune17.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

regimes909.0ms

Accuracy

41.3% (4.5b remaining)

Error of 8.6b against oracle of 4.1b and baseline of 11.7b

bsearch3.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
026867
136867
done36867

end0.0ms

sample1.6s

Algorithm
intervals
Results
792.0ms7699×body80valid
139.0ms264×body1280valid
137.0ms526×body640valid
88.0ms395×body320valid
29.0ms248×body160valid
6.0ms19×body2560valid