Details

Time bar (total: 22.8s)

sample58.0ms

Algorithm
intervals
Results
18.0ms248×body80valid
4.0ms15×body640valid
3.0ms9×body1280valid
3.0ms14×body320valid
1.0ms9×body160valid
1.0ms2×body2560valid

simplify6.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01113
12313
24612
312812
436012
587712
6201612
7358612
done500012

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

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:
25.0ms
(/ (- t x) (- a z))
0.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

series213.0ms

Counts
2 → 6
Calls
2 calls:
87.0ms
(/ (- t x) (- a z))
125.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.5s

Counts
70 → 70
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0118918
1269890
2658838
31743834
done5000830

prune291.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

localize13.0ms

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)

rewrite73.0ms

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:
33.0ms
(/ (- a z) (- t x))
26.0ms
(/ 1 (/ (- a z) (- t x)))
0.0ms
(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

series614.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(/ (- a z) (- t x))
360.0ms
(/ 1 (/ (- a z) (- t x)))
182.0ms
(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

simplify3.1s

Counts
223 → 223
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02743778
16173266
214252943
340152863
done50012861

prune538.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.9b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite167.0ms

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:
46.0ms
(/ (- t x) (- a z))
24.0ms
(+ (* (- y z) (/ (- t x) (- a z))) x)
86.0ms
(* (- y z) (/ (- t x) (- a z)))

series502.0ms

Counts
3 → 9
Calls
3 calls:
81.0ms
(/ (- t x) (- a z))
240.0ms
(+ (* (- y z) (/ (- t x) (- a z))) x)
182.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify1.5s

Counts
135 → 135
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01891881
14851765
217651669
done50011667

prune551.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.6b

localize41.0ms

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
(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

rewrite673.0ms

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:
8.0ms
(cbrt (- t x))
9.0ms
(cbrt (- t x))
186.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
463.0ms
(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

series1.2s

Counts
4 → 12
Calls
4 calls:
242.0ms
(cbrt (- t x))
240.0ms
(cbrt (- t x))
467.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
288.0ms
(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

simplify1.8s

Counts
106 → 106
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02562637
16872520
224951857
done50001713

prune568.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.6b

regimes550.0ms

Accuracy

13.3% (7.5b remaining)

Error of 11.2b against oracle of 3.7b and baseline of 12.3b

bsearch194.0ms

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

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02788
13255
done3255

end0.0ms

sample1.9s

Algorithm
intervals
Results
958.0ms7717×body80valid
135.0ms493×body640valid
72.0ms286×body1280valid
63.0ms403×body320valid
56.0ms269×body160valid
7.0ms23×body2560valid