Details

Time bar (total: 25.9s)

sample48.0ms

Algorithm
intervals
Results
20.0ms258×body80valid
3.0ms13×body640valid
2.0ms7×body1280valid
1.0ms9×body320valid
0.0ms3×body160valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
011245
123245
244245
3122245
4334245
5935245
63616245
done5000245

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
0.9b
(+ x (* (- y z) (/ (- t x) (- a z))))
6.3b
(* (- y z) (/ (- t x) (- a z)))

rewrite101.0ms

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-cbrt-cube add-exp-log
5×pow1 associate-/r* flip3-- associate-*l* flip-- associate-/l* add-log-exp
4×associate-/r/
2×frac-times cbrt-undiv div-exp associate-*l/ prod-exp cbrt-unprod div-inv unswap-sqr associate-/l/
1×+-commutative clear-num sum-log frac-2neg flip3-+ div-sub pow-prod-down associate-*r/ *-commutative flip-+
Counts
3 → 119
Calls
3 calls:
18.0ms
(/ (- t x) (- a z))
12.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
67.0ms
(* (- y z) (/ (- t x) (- a z)))

series385.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(/ (- t x) (- a z))
175.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
151.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify2.3s

Counts
128 → 128
Iterations

Useful iterations: 2 (577.0ms)

IterNodesCost
018336464
150033510
2268932944
done500232944

prune639.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
2.7b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.3b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite219.0ms

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-*l/ associate-*r/
3×pow-prod-down
2×pow-sqr *-commutative pow-prod-up div-inv
1×pow2 +-commutative sum-log flip3-+ pow-plus flip-+
Counts
4 → 175
Calls
4 calls:
5.0ms
(cbrt (- a z))
52.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
141.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series951.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(cbrt (- a z))
152.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
416.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
196.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify3.0s

Counts
187 → 187
Iterations

Useful iterations: done (3.0s)

IterNodesCost
030778961
187970930
2444170348
done500164308

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (- t x)) (cbrt (- t x)))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
1.3b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
5.3b
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
58×add-sqr-sqrt
56×cbrt-prod
52×*-un-lft-identity
33×associate-*l*
30×flip3-- flip--
29×add-exp-log
28×frac-times
23×pow1
22×add-cube-cbrt
20×swap-sqr
18×associate-*r/
17×associate-*r*
15×add-cbrt-cube
13×prod-exp cbrt-unprod distribute-lft-out--
12×pow1/3
11×associate-*l/
10×unswap-sqr
9×difference-of-squares
8×associate-/r/
7×pow-prod-down
6×times-frac add-log-exp
4×cbrt-undiv div-exp pow-sqr pow-prod-up
3×*-commutative
2×pow2 pow-plus
1×+-commutative sum-log flip3-+ flip-+ div-inv
Counts
4 → 182
Calls
4 calls:
45.0ms
(* (cbrt (- t x)) (cbrt (- t x)))
43.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
158.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
6.0ms
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
180.0ms
(* (cbrt (- t x)) (cbrt (- t x)))
187.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
575.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
223.0ms
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify3.2s

Counts
194 → 194
Iterations

Useful iterations: done (3.1s)

IterNodesCost
033187279
189275313
2406374387
done500071267

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.9b

localize86.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
2.7b
(* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))
6.0b
(+ x (* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))

rewrite407.0ms

Algorithm
rewrite-expression-head
Rules
358×cbrt-div
141×frac-times
116×flip3-- flip--
97×associate-*l*
88×add-sqr-sqrt
82×associate-/r/
78×*-un-lft-identity
59×cbrt-prod
54×associate-*r*
47×times-frac associate-*l/ associate-*r/
38×add-exp-log
34×add-cube-cbrt
24×add-cbrt-cube
21×distribute-lft-out--
19×difference-of-squares
15×prod-exp cbrt-unprod
13×pow1
10×cbrt-undiv swap-sqr div-exp
7×pow1/3 unswap-sqr
6×add-log-exp
3×pow-prod-down
2×pow-sqr *-commutative pow-prod-up div-inv
1×pow2 +-commutative sum-log flip3-+ pow-plus flip-+
Counts
4 → 248
Calls
4 calls:
3.0ms
(cbrt (- a z))
33.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
339.0ms
(* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))
10.0ms
(+ x (* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
218.0ms
(cbrt (- a z))
206.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
395.0ms
(* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))
184.0ms
(+ x (* (/ (- y z) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))

simplify1.9s

Counts
260 → 260
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0430156989
11316143868
done5001143086

prune2.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.9b

regimes985.0ms

Accuracy

57.1% (3.4b remaining)

Error of 7.6b against oracle of 4.1b and baseline of 12.1b

bsearch4.0ms

simplify19.0ms

Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0321187
1431187
done431187

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s7795×body80valid
133.0ms488×body640valid
108.0ms287×body1280valid
60.0ms393×body320valid
29.0ms249×body160valid
4.0ms16×body2560valid