Details

Time bar (total: 20.9s)

sample39.0ms

Algorithm
intervals
Results
14.0ms248×body80valid
3.0ms15×body640valid
2.0ms14×body320valid
2.0ms9×body1280valid
1.0ms9×body160valid
1.0ms2×body2560valid

simplify6.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01113
12313
24612
312812
436012
587712
6201612
7358612
done500012

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
16.1b
(fma (/ (- t x) (- a z)) (- y z) x)

rewrite45.0ms

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:
40.0ms
(/ (- t x) (- a z))
0.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

series248.0ms

Counts
2 → 6
Calls
2 calls:
80.0ms
(/ (- t x) (- a z))
168.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.2s

Counts
70 → 70
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0118918
1269890
2658838
31743834
done5000830

prune231.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- a z) (- t x))
0.4b
(/ 1 (/ (- a z) (- t x)))
16.0b
(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
218×times-frac
195×add-sqr-sqrt *-un-lft-identity
91×add-cube-cbrt
52×distribute-lft-out-- difference-of-squares
36×associate-/r*
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp associate-/l*
6×flip3-- flip-- div-inv
4×pow1 cbrt-undiv
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp clear-num associate-/l/
1×pow-flip div-sub fma-udef inv-pow
Counts
3 → 214
Calls
3 calls:
44.0ms
(/ (- a z) (- t x))
42.0ms
(/ 1 (/ (- a z) (- t x)))
1.0ms
(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

series556.0ms

Counts
3 → 9
Calls
3 calls:
86.0ms
(/ (- a z) (- t x))
319.0ms
(/ 1 (/ (- a z) (- t x)))
151.0ms
(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

simplify3.2s

Counts
223 → 223
Iterations

Useful iterations: done (3.2s)

IterNodesCost
02743778
16173266
214252943
340152863
done50012861

prune512.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
4.4b
(+ x (* (- y z) (/ (- t x) (- a z))))
5.3b
(* (- y z) (/ (- t x) (- a z)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
74×*-un-lft-identity
51×times-frac
31×associate-*r*
28×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 fma-def log1p-expm1-u
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 128
Calls
3 calls:
27.0ms
(/ (- t x) (- a z))
8.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
89.0ms
(* (- y z) (/ (- t x) (- a z)))

series513.0ms

Counts
3 → 9
Calls
3 calls:
101.0ms
(/ (- t x) (- a z))
231.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
181.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify1.3s

Counts
137 → 137
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01891881
14841769
217871659
done50021657

prune500.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
1.0b
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
10.3b
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
18×add-sqr-sqrt
16×cbrt-div
15×*-un-lft-identity
14×add-cbrt-cube
13×associate-*r*
10×cbrt-prod flip3-- flip--
9×add-cube-cbrt prod-exp cbrt-unprod
8×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×fma-def associate-*r/ distribute-lft-out-- difference-of-squares
2×times-frac pow1/3 unswap-sqr
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+ div-inv
Counts
4 → 96
Calls
4 calls:
5.0ms
(cbrt (- t x))
8.0ms
(cbrt (- t x))
154.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
17.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
186.0ms
(cbrt (- t x))
189.0ms
(cbrt (- t x))
466.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
201.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify1.8s

Counts
108 → 108
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02562637
16872502
225281845
done50011705

prune487.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.6b

regimes502.0ms

Accuracy

11.3% (7.4b remaining)

Error of 11.1b against oracle of 3.7b and baseline of 12.1b

bsearch157.0ms

Steps
ItersRangePoint
9
1.3374241406868578e-181
7.684784638948536e-174
4.324311520218843e-174
8
-3.8032487866059233e-25
-6.0695810582136045e-28
-6.14323213192593e-28

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02690
13456
done3456

end0.0ms

sample1.5s

Algorithm
intervals
Results
672.0ms7717×body80valid
155.0ms493×body640valid
148.0ms286×body1280valid
70.0ms403×body320valid
31.0ms269×body160valid
8.0ms23×body2560valid