Details

Time bar (total: 23.3s)

sample49.0ms

Algorithm
intervals
Results
17.0ms246×body80valid
4.0ms15×body640valid
4.0ms12×body1280valid
2.0ms10×body320valid
1.0ms10×body160valid

simplify9.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
01113
12013
24513
311612
432212
577012
6155612
7286512
8469812
done500012

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- y x) (- a t))
14.2b
(fma (/ (- y x) (- a t)) (- z t) x)

rewrite38.0ms

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:
35.0ms
(/ (- y x) (- a t))
0.0ms
(fma (/ (- y x) (- a t)) (- z t) x)

series247.0ms

Counts
2 → 6
Calls
2 calls:
99.0ms
(/ (- y x) (- a t))
147.0ms
(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.8s

Counts
70 → 70
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0118918
1270890
2658838
31740836
done5000830

prune321.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- y x) (- a t))
3.1b
(+ (* (/ (- y x) (- a t)) (- z t)) x)
6.6b
(* (/ (- y x) (- a t)) (- z t))

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
102×add-sqr-sqrt
97×*-un-lft-identity
51×add-cube-cbrt times-frac
36×prod-diff
31×associate-*l*
23×distribute-lft-out-- difference-of-squares
22×distribute-rgt-in associate-+l+ distribute-lft-in
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*r* associate-/r* flip-- associate-/l* add-log-exp
4×sub-neg associate-/r/
3×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative fma-def frac-2neg flip3-+ div-sub pow-prod-down associate-*l/ clear-num sum-log *-commutative flip-+
Counts
3 → 170
Calls
3 calls:
47.0ms
(/ (- y x) (- a t))
63.0ms
(+ (* (/ (- y x) (- a t)) (- z t)) x)
103.0ms
(* (/ (- y x) (- a t)) (- z t))

series762.0ms

Counts
3 → 9
Calls
3 calls:
97.0ms
(/ (- y x) (- a t))
259.0ms
(+ (* (/ (- y x) (- a t)) (- z t)) x)
406.0ms
(* (/ (- y x) (- a t)) (- z t))

simplify1.7s

Counts
179 → 179
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02563107
16672740
219392516
done50012490

prune780.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- z t) (- a t))
1.6b
(* (- y x) (/ (- z t) (- a t)))
2.2b
(+ (* (- y x) (/ (- z t) (- a t))) x)

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
73×*-un-lft-identity
51×times-frac
31×associate-*r*
27×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
3×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative fma-def frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 126
Calls
3 calls:
42.0ms
(/ (- z t) (- a t))
119.0ms
(* (- y x) (/ (- z t) (- a t)))
45.0ms
(+ (* (- y x) (/ (- z t) (- a t))) x)

series601.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(/ (- z t) (- a t))
204.0ms
(* (- y x) (/ (- z t) (- a t)))
315.0ms
(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify1.3s

Counts
135 → 135
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01891881
14871765
217691669
done50001667

prune915.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- a t))
0.2b
(* (- z t) (/ 1 (- a t)))
1.6b
(* (- y x) (* (- z t) (/ 1 (- a t))))
3.1b
(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
44×*-un-lft-identity
32×add-exp-log times-frac
25×add-cube-cbrt
22×associate-*r*
20×frac-times add-cbrt-cube
17×flip3-- flip--
13×prod-exp
12×pow1
10×associate-*r/ associate-*l* associate-*l/
9×distribute-lft-out-- difference-of-squares
7×cbrt-unprod
6×div-exp add-log-exp
5×associate-/r*
4×expm1-log1p-u pow-prod-down associate-/r/ un-div-inv log1p-expm1-u
3×cbrt-undiv rec-exp 1-exp associate-/l* unswap-sqr
2×*-commutative div-inv
1×+-commutative pow-flip fma-def frac-2neg flip3-+ clear-num sum-log flip-+ inv-pow
Counts
4 → 155
Calls
4 calls:
20.0ms
(/ 1 (- a t))
61.0ms
(* (- z t) (/ 1 (- a t)))
96.0ms
(* (- y x) (* (- z t) (/ 1 (- a t))))
94.0ms
(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

series596.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ 1 (- a t))
85.0ms
(* (- z t) (/ 1 (- a t)))
195.0ms
(* (- y x) (* (- z t) (/ 1 (- a t))))
252.0ms
(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

simplify1.5s

Counts
167 → 167
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02292378
15821960
221521782
done50021780

prune647.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.5b

regimes476.0ms

Accuracy

14.3% (7.2b remaining)

Error of 10.8b against oracle of 3.6b and baseline of 11.9b

bsearch98.0ms

Steps
ItersRangePoint
8
1.3793369693960326e-72
5.420309125457467e-70
1.4749780862081662e-72
3
-1.350252423850461e-228
-1.1088529455719019e-228
-1.3220215613054517e-228

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02246
12834
done2834

end0.0ms

sample1.4s

Algorithm
intervals
Results
662.0ms7755×body80valid
130.0ms423×body320valid
103.0ms477×body640valid
77.0ms288×body1280valid
76.0ms272×body160valid
4.0ms13×body2560valid