Details

Time bar (total: 15.6s)

sample26.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
1.0ms11×body640valid
1.0ms9×body1280valid
1.0ms13×body320valid
1.0ms11×body160valid
0.0ms1×body2560valid

simplify6.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01113
12313
24313
311513
426313
556813
6100413
7172813
8278213
9352413
10375913
11435413
done500013

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
5.0b
(+ x (* (- y z) (/ (- t x) (- a z))))
6.2b
(* (- y z) (/ (- t x) (- a z)))

rewrite51.0ms

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/
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 → 119
Calls
3 calls:
11.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
33.0ms
(* (- y z) (/ (- t x) (- a z)))

series330.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(/ (- t x) (- a z))
148.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
129.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify763.0ms

Counts
128 → 128
Iterations

Useful iterations: 2 (155.0ms)

IterNodesCost
01831813
14741704
216931606
done50001606

prune330.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.5b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
7.9b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
78×*-un-lft-identity
60×cbrt-prod
54×associate-*r*
52×times-frac
34×add-cube-cbrt
28×cbrt-div
27×add-exp-log
25×associate-*l*
21×distribute-lft-out--
19×difference-of-squares
18×add-cbrt-cube
14×flip3-- flip--
13×pow1
10×swap-sqr associate-/r/ unswap-sqr
9×frac-times prod-exp cbrt-unprod
7×cbrt-undiv pow1/3 div-exp
6×add-log-exp
5×associate-*r/ associate-*l/
3×pow-prod-down
2×pow-sqr *-commutative pow-prod-up div-inv
1×+-commutative pow2 flip3-+ pow-plus sum-log flip-+
Counts
4 → 175
Calls
4 calls:
2.0ms
(cbrt (- a z))
81.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
20.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
3.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series717.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(cbrt (- a z))
292.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
126.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
151.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify1.2s

Counts
187 → 187
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03074004
18423733
236363184
done50003171

prune561.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
7.7b
(+ x (* (/ (- y z) (* (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (- a z)))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
84×cbrt-prod
76×add-sqr-sqrt
70×*-un-lft-identity
36×cbrt-div
30×swap-sqr
28×add-cube-cbrt
25×pow1
24×associate-*r* associate-*l*
18×flip3-- pow1/3 flip-- distribute-lft-out--
12×frac-times difference-of-squares unswap-sqr
10×add-exp-log
6×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up add-log-exp
4×add-cbrt-cube
3×pow2 pow-plus prod-exp *-commutative cbrt-unprod
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 179
Calls
4 calls:
21.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
23.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
21.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
3.0ms
(+ x (* (/ (- y z) (* (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (- a z)))))

series520.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
121.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
122.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
154.0ms
(+ x (* (/ (- y z) (* (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (- a z)))))

simplify459.0ms

Counts
191 → 191
Iterations

Useful iterations: done (453.0ms)

IterNodesCost
01393370
13083050
210182554
done50012550

prune598.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 3.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.5b
(cbrt (- a z))
1.2b
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
4.5b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
35×add-cbrt-cube
32×prod-exp cbrt-unprod
22×cbrt-undiv div-exp
15×cbrt-prod add-sqr-sqrt *-un-lft-identity
14×associate-*l*
9×pow1 add-cube-cbrt
8×times-frac
6×cbrt-div add-log-exp
5×frac-times associate-*r/
3×flip3-- pow-prod-down associate-*l/ flip-- distribute-lft-out-- difference-of-squares
2×pow1/3 associate-/r/
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ div-inv
Counts
4 → 103
Calls
4 calls:
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
93.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series751.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(cbrt (- a z))
149.0ms
(cbrt (- a z))
301.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
152.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify745.0ms

Counts
115 → 115
Iterations

Useful iterations: done (742.0ms)

IterNodesCost
02113755
16293550
222432460
done50011913

prune315.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 3.3b

regimes428.0ms

Accuracy

54.3% (4.1b remaining)

Error of 7.5b against oracle of 3.4b and baseline of 12.4b

bsearch3.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02891
13768
done3768

end0.0ms

sample687.0ms

Algorithm
intervals
Results
257.0ms7756×body80valid
61.0ms492×body640valid
44.0ms278×body1280valid
35.0ms393×body320valid
16.0ms263×body160valid
4.0ms19×body2560valid