Details

Time bar (total: 18.7s)

sample25.0ms

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

simplify7.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01113
12313
24313
311513
426313
556813
6100413
7171613
8307413
9381213
10406513
11437813
done500113

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize10.0ms

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)))

rewrite53.0ms

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:
14.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
32.0ms
(* (- y z) (/ (- t x) (- a z)))

series330.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(/ (- t x) (- a z))
151.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
129.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify721.0ms

Counts
128 → 128
Iterations

Useful iterations: 2 (261.0ms)

IterNodesCost
01831813
14741704
216871606
done50011606

prune324.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- a z) (- t x))
0.4b
(/ 1 (/ (- a z) (- t x)))
5.7b
(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
6.2b
(* (- y z) (/ 1 (/ (- a z) (- t x))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
392×times-frac
338×add-sqr-sqrt
326×*-un-lft-identity
158×add-cube-cbrt
98×associate-*r*
83×distribute-lft-out-- difference-of-squares
36×add-exp-log associate-/r*
20×add-cbrt-cube
18×associate-/r/
15×div-exp
11×flip3-- flip--
10×div-inv
8×associate-/l*
7×pow1 cbrt-undiv prod-exp
6×add-log-exp
5×associate-*l* unswap-sqr
4×rec-exp 1-exp
3×cbrt-unprod
2×frac-times frac-2neg associate-*l/ clear-num associate-/l/
1×+-commutative pow-flip flip3-+ div-sub associate-*r/ pow-prod-down sum-log un-div-inv *-commutative flip-+ inv-pow
Counts
4 → 344
Calls
4 calls:
10.0ms
(/ (- a z) (- t x))
14.0ms
(/ 1 (/ (- a z) (- t x)))
2.0ms
(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
62.0ms
(* (- y z) (/ 1 (/ (- a z) (- t x))))

series703.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (- a z) (- t x))
197.0ms
(/ 1 (/ (- a z) (- t x)))
155.0ms
(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
298.0ms
(* (- y z) (/ 1 (/ (- a z) (- t x))))

simplify1.3s

Counts
356 → 356
Iterations

Useful iterations: 2 (764.0ms)

IterNodesCost
03936138
110135012
227024609
done50014609

prune672.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- y z) (- a z))
0.2b
(/ (cbrt 1) (/ 1 (- t x)))
1.5b
(* (/ (- y z) (- a z)) (/ (cbrt 1) (/ 1 (- t x))))
5.2b
(+ x (* (/ (- y z) (- a z)) (/ (cbrt 1) (/ 1 (- t x)))))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
537×times-frac
421×add-sqr-sqrt
365×*-un-lft-identity
231×add-cube-cbrt
141×cbrt-prod
131×associate-*r*
61×distribute-lft-out-- difference-of-squares
50×add-exp-log
32×associate-/r/
31×associate-*l*
26×associate-/r* add-cbrt-cube
24×div-exp
20×unswap-sqr
17×div-inv
16×flip3-- flip--
13×cbrt-undiv
11×associate-/l*
10×prod-exp
6×pow1 cbrt-unprod add-log-exp
3×rec-exp 1-exp
2×frac-2neg clear-num associate-/l/
1×+-commutative frac-times flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative flip-+
Counts
4 → 443
Calls
4 calls:
11.0ms
(/ (- y z) (- a z))
12.0ms
(/ (cbrt 1) (/ 1 (- t x)))
114.0ms
(* (/ (- y z) (- a z)) (/ (cbrt 1) (/ 1 (- t x))))
2.0ms
(+ x (* (/ (- y z) (- a z)) (/ (cbrt 1) (/ 1 (- t x)))))

series523.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (- y z) (- a z))
18.0ms
(/ (cbrt 1) (/ 1 (- t x)))
300.0ms
(* (/ (- y z) (- a z)) (/ (cbrt 1) (/ 1 (- t x))))
154.0ms
(+ x (* (/ (- y z) (- a z)) (/ (cbrt 1) (/ 1 (- t x)))))

simplify1.4s

Counts
455 → 455
Iterations

Useful iterations: 2 (906.0ms)

IterNodesCost
05388922
116405412
232355102
done50005102

prune730.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
1.5b
(* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (cbrt (- y z)) (cbrt (- a z)))) (/ (cbrt 1) (/ 1 (- t x))))
5.2b
(+ x (* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (cbrt (- y z)) (cbrt (- a z)))) (/ (cbrt 1) (/ 1 (- t x)))))

rewrite315.0ms

Algorithm
rewrite-expression-head
Rules
326×add-exp-log
216×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity
146×prod-exp
139×associate-*r*
131×div-exp
110×add-cube-cbrt
96×cbrt-prod add-cbrt-cube
88×cbrt-unprod
72×cbrt-undiv
25×distribute-lft-out--
23×difference-of-squares
16×pow1
14×cbrt-div
13×flip3-- associate-/r/ flip--
11×rec-exp 1-exp
10×swap-sqr
9×frac-times associate-*l*
7×pow1/3 associate-*l/ div-inv
6×add-log-exp
5×associate-*r/ pow-prod-down
4×unswap-sqr
2×pow-sqr *-commutative pow-prod-up
1×+-commutative pow2 flip3-+ pow-plus sum-log flip-+
Counts
4 → 319
Calls
4 calls:
2.0ms
(cbrt (- a z))
19.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
265.0ms
(* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (cbrt (- y z)) (cbrt (- a z)))) (/ (cbrt 1) (/ 1 (- t x))))
2.0ms
(+ x (* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (cbrt (- y z)) (cbrt (- a z)))) (/ (cbrt 1) (/ 1 (- t x)))))

series757.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(cbrt (- a z))
126.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
310.0ms
(* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (cbrt (- y z)) (cbrt (- a z)))) (/ (cbrt 1) (/ 1 (- t x))))
163.0ms
(+ x (* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (cbrt (- y z)) (cbrt (- a z)))) (/ (cbrt 1) (/ 1 (- t x)))))

simplify1.1s

Counts
331 → 331
Iterations

Useful iterations: done (1.1s)

IterNodesCost
058813184
1191411059
done500110063

prune773.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.1b

regimes311.0ms

Accuracy

15.4% (6.4b remaining)

Error of 10.5b against oracle of 4.2b and baseline of 11.7b

bsearch116.0ms

Steps
ItersRangePoint
10
1.422627522925298e-211
2.8974098557973016e-195
6.607165126286426e-200
9
-1.7500594794839567e-124
-1.6036634392402047e-131
-2.8613728432926933e-131

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02757
13740
done3740

end0.0ms

sample692.0ms

Algorithm
intervals
Results
249.0ms7756×body80valid
59.0ms492×body640valid
44.0ms393×body320valid
41.0ms278×body1280valid
18.0ms263×body160valid
4.0ms19×body2560valid