Details

Time bar (total: 23.2s)

sample36.0ms

Algorithm
intervals
Results
10.0ms246×body80valid
2.0ms14×body640valid
2.0ms15×body320valid
1.0ms7×body1280valid
1.0ms9×body160valid

simplify9.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (33.0ms)

IterNodesCost
01113
12013
24513
311612
432212
577012
6155612
7286512
8469812
done500012

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.6b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- y x) (- a t))
14.3b
(fma (/ (- y x) (- a t)) (- z t) x)

rewrite58.0ms

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:
52.0ms
(/ (- y x) (- a t))
1.0ms
(fma (/ (- y x) (- a t)) (- z t) x)

series301.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(/ (- y x) (- a t))
215.0ms
(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.5s

Counts
70 → 70
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0118918
1270890
2658838
31740836
done5000830

prune275.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- y x) (- a t))
4.0b
(+ (* (/ (- y x) (- a t)) (- z t)) x)
6.1b
(* (/ (- y x) (- a t)) (- z t))

rewrite185.0ms

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:
33.0ms
(/ (- y x) (- a t))
59.0ms
(+ (* (/ (- y x) (- a t)) (- z t)) x)
84.0ms
(* (/ (- y x) (- a t)) (- z t))

series665.0ms

Counts
3 → 9
Calls
3 calls:
80.0ms
(/ (- y x) (- a t))
250.0ms
(+ (* (/ (- y x) (- a t)) (- z t)) x)
335.0ms
(* (/ (- y x) (- a t)) (- z t))

simplify1.6s

Counts
179 → 179
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02563107
16672740
219392516
done50012490

prune609.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.7b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- z t) (- a t))
2.5b
(* (- y x) (/ (- z t) (- a t)))
2.8b
(+ (* (- y x) (/ (- z t) (- a t))) x)

rewrite213.0ms

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:
27.0ms
(/ (- z t) (- a t))
113.0ms
(* (- y x) (/ (- z t) (- a t)))
61.0ms
(+ (* (- y x) (/ (- z t) (- a t))) x)

series522.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(/ (- z t) (- a t))
179.0ms
(* (- y x) (/ (- z t) (- a t)))
271.0ms
(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify1.6s

Counts
135 → 135
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01891881
14871765
217691669
done50001667

prune523.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- a t))
0.2b
(* (- z t) (/ 1 (- a t)))
2.5b
(* (- y x) (* (- z t) (/ 1 (- a t))))
4.5b
(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

rewrite282.0ms

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:
25.0ms
(/ 1 (- a t))
74.0ms
(* (- z t) (/ 1 (- a t)))
83.0ms
(* (- y x) (* (- z t) (/ 1 (- a t))))
90.0ms
(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

series666.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ 1 (- a t))
109.0ms
(* (- z t) (/ 1 (- a t)))
218.0ms
(* (- y x) (* (- z t) (/ 1 (- a t))))
292.0ms
(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

simplify1.5s

Counts
167 → 167
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02292378
15821960
221521782
done50021780

prune583.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.7b

regimes398.0ms

Accuracy

14.6% (6.8b remaining)

Error of 10.6b against oracle of 3.8b and baseline of 11.8b

bsearch161.0ms

Steps
ItersRangePoint
7
1.270532878618462e-164
1.8595605403829251e-162
1.8315839196138794e-164
10
-9.075518483702745e-141
-5.89973422929116e-153
-1.5730863727778726e-148

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02748
13548
done3548

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.1s7820×body80valid
169.0ms432×body320valid
102.0ms482×body640valid
67.0ms249×body1280valid
30.0ms262×body160valid
7.0ms20×body2560valid