Details

Time bar (total: 21.8s)

sample48.0ms

Algorithm
intervals
Results
15.0ms241×body80valid
3.0ms13×body640valid
2.0ms12×body320valid
2.0ms14×body160valid
1.0ms5×body1280valid
1.0ms2×body2560valid

simplify8.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
01113
12013
24513
311612
432212
577012
6155612
7286512
8469812
done500012

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- y x) (- a t))
13.9b
(fma (/ (- y x) (- a t)) (- z t) x)

rewrite27.0ms

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:
24.0ms
(/ (- y x) (- a t))
0.0ms
(fma (/ (- y x) (- a t)) (- z t) x)

series182.0ms

Counts
2 → 6
Calls
2 calls:
74.0ms
(/ (- y x) (- a t))
108.0ms
(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.3s

Counts
70 → 70
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0118918
1270890
2658838
31740836
done5000830

prune230.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.5b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- a t))
0.2b
(* (- y x) (/ 1 (- a t)))
13.9b
(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite110.0ms

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:
26.0ms
(/ 1 (- a t))
77.0ms
(* (- y x) (/ 1 (- a t)))
1.0ms
(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series239.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(/ 1 (- a t))
68.0ms
(* (- y x) (/ 1 (- a t)))
120.0ms
(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify2.2s

Counts
114 → 114
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01551285
13451052
2954948
33237946
done5001946

prune358.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 6.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- y x) (- a t))
4.7b
(* (- z t) (/ (- y x) (- a t)))
5.0b
(+ (* (- z t) (/ (- y x) (- a t))) x)

rewrite172.0ms

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
(/ (- y x) (- a t))
88.0ms
(* (- z t) (/ (- y x) (- a t)))
48.0ms
(+ (* (- z t) (/ (- y x) (- a t))) x)

series469.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(/ (- y x) (- a t))
186.0ms
(* (- z t) (/ (- y x) (- a t)))
194.0ms
(+ (* (- z t) (/ (- y x) (- a t))) x)

simplify1.1s

Counts
135 → 135
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01891881
14861765
217681669
done50011667

prune487.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 3.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- y x))
0.6b
(cbrt (- y x))
0.8b
(* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))))
8.4b
(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

rewrite520.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
17×add-sqr-sqrt
16×cbrt-div
14×*-un-lft-identity add-cbrt-cube
13×associate-*r*
10×cbrt-prod flip3-- flip--
9×prod-exp cbrt-unprod
8×add-cube-cbrt associate-/r/
6×pow1 frac-times add-log-exp
5×associate-*l*
4×cbrt-undiv expm1-log1p-u div-exp associate-*l/ log1p-expm1-u
3×associate-*r/ distribute-lft-out-- difference-of-squares
2×times-frac pow1/3 unswap-sqr
1×+-commutative fma-def flip3-+ pow-prod-down sum-log *-commutative flip-+ div-inv
Counts
4 → 94
Calls
4 calls:
6.0ms
(cbrt (- y x))
5.0ms
(cbrt (- y x))
139.0ms
(* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))))
367.0ms
(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

series1.1s

Counts
4 → 12
Calls
4 calls:
226.0ms
(cbrt (- y x))
214.0ms
(cbrt (- y x))
405.0ms
(* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))))
218.0ms
(+ (* (* (- z t) (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt (- y x)) (cbrt (- a t)))) x)

simplify1.8s

Counts
106 → 106
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02562637
16882520
224941866
done50021722

prune465.0ms

Pruning

21 alts after pruning (18 fresh and 3 done)

Merged error: 3.6b

regimes551.0ms

Accuracy

23.5% (7.0b remaining)

Error of 10.7b against oracle of 3.6b and baseline of 12.8b

bsearch148.0ms

Steps
ItersRangePoint
8
2.0007789822909896e-198
1.0099514213797079e-194
3.085625866310274e-197
7
-5.925413525790681e-145
-6.231127244252839e-147
-5.181595524895995e-145

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
034102
142102
done42102

end0.0ms

sample1.9s

Algorithm
intervals
Results
888.0ms7591×body80valid
139.0ms500×body640valid
113.0ms289×body1280valid
105.0ms423×body320valid
55.0ms288×body160valid
7.0ms23×body2560valid