Details

Time bar (total: 23.3s)

sample80.0ms

Algorithm
intervals
Results
32.0ms246×body80valid
5.0ms14×body640valid
3.0ms15×body320valid
3.0ms7×body1280valid
1.0ms9×body160valid

simplify9.0s

Counts
1 → 1
Iterations

Useful iterations: 3 (33.0ms)

IterNodesCost
01113
12013
24513
311612
432212
577012
6155612
7286512
8469812
done500012

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.6b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite54.0ms

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:
49.0ms
(/ (- y x) (- a t))
1.0ms
(fma (/ (- y x) (- a t)) (- z t) x)

series225.0ms

Counts
2 → 6
Calls
2 calls:
84.0ms
(/ (- y x) (- a t))
141.0ms
(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.6s

Counts
70 → 70
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0118918
1270890
2658838
31740836
done5000830

prune316.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize23.0ms

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))

rewrite241.0ms

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:
46.0ms
(/ (- y x) (- a t))
43.0ms
(+ (* (/ (- y x) (- a t)) (- z t)) x)
144.0ms
(* (/ (- y x) (- a t)) (- z t))

series796.0ms

Counts
3 → 9
Calls
3 calls:
113.0ms
(/ (- y x) (- a t))
288.0ms
(+ (* (/ (- y x) (- a t)) (- z t)) x)
395.0ms
(* (/ (- y x) (- a t)) (- z t))

simplify1.6s

Counts
179 → 179
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02563107
16672740
219392516
done50012490

prune750.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.7b

localize24.0ms

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)

rewrite178.0ms

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:
32.0ms
(/ (- z t) (- a t))
92.0ms
(* (- y x) (/ (- z t) (- a t)))
48.0ms
(+ (* (- y x) (/ (- z t) (- a t))) x)

series568.0ms

Counts
3 → 9
Calls
3 calls:
99.0ms
(/ (- z t) (- a t))
196.0ms
(* (- y x) (/ (- z t) (- a t)))
273.0ms
(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify1.4s

Counts
135 → 135
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01891881
14871765
217691669
done50001667

prune619.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.7b

localize14.0ms

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)

rewrite284.0ms

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:
17.0ms
(/ 1 (- a t))
74.0ms
(* (- z t) (/ 1 (- a t)))
98.0ms
(* (- y x) (* (- z t) (/ 1 (- a t))))
89.0ms
(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

series685.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ 1 (- a t))
102.0ms
(* (- z t) (/ 1 (- a t)))
236.0ms
(* (- y x) (* (- z t) (/ 1 (- a t))))
280.0ms
(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

simplify1.7s

Counts
167 → 167
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02292378
15821960
221521782
done50021780

prune529.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.7b

regimes359.0ms

Accuracy

14.6% (6.8b remaining)

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

bsearch158.0ms

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

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02748
13548
done3548

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.1s7820×body80valid
135.0ms482×body640valid
91.0ms249×body1280valid
70.0ms432×body320valid
30.0ms262×body160valid
6.0ms20×body2560valid