Details

Time bar (total: 14.1s)

sample31.0ms

Algorithm
intervals
Results
8.0ms264×body80valid
3.0ms22×body640valid
1.0ms10×body1280valid
1.0ms13×body320valid
1.0ms12×body160valid

simplify4.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01113
12313
24612
312812
436012
587712
6201612
7358612
done500012

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
15.8b
(fma (/ (- t x) (- a z)) (- y z) x)

rewrite25.0ms

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:
23.0ms
(/ (- t x) (- a z))
0.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

series155.0ms

Counts
2 → 6
Calls
2 calls:
58.0ms
(/ (- t x) (- a z))
97.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.0s

Counts
70 → 70
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0118918
1269890
2658838
31743834
done5000830

prune211.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- a z))
0.3b
(* (- t x) (/ 1 (- a z)))
15.8b
(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite63.0ms

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:
12.0ms
(/ 1 (- a z))
46.0ms
(* (- t x) (/ 1 (- a z)))
0.0ms
(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series190.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(/ 1 (- a z))
56.0ms
(* (- t x) (/ 1 (- a z)))
96.0ms
(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify1.7s

Counts
114 → 114
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01551285
13441052
2954948
33231944
done5000942

prune246.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
4.3b
(* (- y z) (/ (- t x) (- a z)))
5.4b
(+ x (* (- y z) (/ (- t x) (- a z))))

rewrite96.0ms

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:
25.0ms
(/ (- t x) (- a z))
57.0ms
(* (- y z) (/ (- t x) (- a z)))
8.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))

series370.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(/ (- t x) (- a z))
145.0ms
(* (- y z) (/ (- t x) (- a z)))
170.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))

simplify951.0ms

Counts
137 → 137
Iterations

Useful iterations: done (948.0ms)

IterNodesCost
01891881
14841769
217901659
done50001657

prune337.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
0.8b
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
10.1b
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite121.0ms

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:
4.0ms
(cbrt (- a z))
4.0ms
(cbrt (- a z))
102.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
8.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series782.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(cbrt (- a z))
148.0ms
(cbrt (- a z))
307.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
170.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify1.2s

Counts
108 → 108
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02542637
16742502
224771845
done50001705

prune371.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.8b

regimes309.0ms

Accuracy

16.8% (7.0b remaining)

Error of 10.6b against oracle of 3.6b and baseline of 12.0b

bsearch106.0ms

Steps
ItersRangePoint
9
8.224624671681947e-55
6.986279115010668e-47
8.392440744553116e-55
9
-1.8642499353850409e-90
-7.813456859551418e-100
-7.952712787195167e-100

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02890
13556
done3556

end0.0ms

sample775.0ms

Algorithm
intervals
Results
249.0ms7807×body80valid
53.0ms484×body640valid
40.0ms273×body1280valid
32.0ms381×body320valid
15.0ms262×body160valid
2.0ms13×body2560valid