Details

sample58.0ms

Algorithm

intervals

Results

17.0ms	235×	body	80	valid
5.0ms	18×	body	640	valid
3.0ms	14×	body	320	valid
2.0ms	6×	body	1280	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3379
5	728
4	242
3	111
2	52
1	22
0	11

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.4b	(fma y (/ (- t z) (- a t)) (+ y x))

rewrite32.0ms

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-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

28.0ms	(/ (- t z) (- a t))
0.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

series261.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (- t z) (- a t))
200.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

simplify2.4s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4441
2	825
1	263
0	114

prune470.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.9b	(+ (* y (/ (- t z) (- a t))) (+ y x))
2.1b	(* y (/ (- t z) (- a t)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1` `associate-/r` `associate-/l`
4×	`associate-/r/`
3×	`expm1-log1p-u` `sum-log` `flip3--` `associate-l` `associate-*r/` `log1p-expm1-u` `flip--`
2×	`cbrt-undiv` `flip3-+` `div-exp` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `associate-+r+` `clear-num` `fma-def` `frac-2neg` `div-sub` `pow-prod-down` `*-commutative`

Counts

3 → 124

Calls

3 calls:

36.0ms	(/ (- t z) (- a t))
49.0ms	(+ (* y (/ (- t z) (- a t))) (+ y x))
37.0ms	(* y (/ (- t z) (- a t)))

series397.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ (- t z) (- a t))
203.0ms	(+ (* y (/ (- t z) (- a t))) (+ y x))
128.0ms	(* y (/ (- t z) (- a t)))

simplify1.9s

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	2457
1	562
0	191

prune828.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
9.7b	(fma y (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) (+ y x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

5.0ms	(cbrt (- t z))
6.0ms	(cbrt (- t z))
6.0ms	(cbrt (- t z))
1.0ms	(fma y (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) (+ y x))

series835.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (- t z))
193.0ms	(cbrt (- t z))
249.0ms	(cbrt (- t z))
187.0ms	(fma y (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) (+ y x))

simplify1.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1641
2	476
1	192
0	94

prune591.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
7.4b	(* (* (* y (cbrt (- t z))) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t)))
7.7b	(+ (* (* (* y (cbrt (- t z))) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) (+ y x))

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

76×	`cbrt-div`
55×	`add-sqr-sqrt` `*-un-lft-identity`
51×	`associate-*r/`
48×	`frac-times`
46×	`associate-r`
40×	`times-frac`
39×	`flip3--` `flip--`
36×	`associate-*l/`
35×	`cbrt-prod`
34×	`frac-add`
25×	`add-exp-log` `add-cube-cbrt`
18×	`flip3-+` `flip-+`
16×	`add-cbrt-cube`
15×	`distribute-lft-out--` `difference-of-squares`
13×	`pow1`
12×	`prod-exp` `cbrt-unprod`
9×	`add-log-exp`
6×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `sum-log` `div-exp`
2×	`pow1/3` `associate-/r/`
1×	`+-commutative` `associate-+r+` `fma-def` `associate-l` `*-commutative` `div-inv`

Counts

4 → 173

Calls

4 calls:

4.0ms	(cbrt (- t z))
3.0ms	(cbrt (- t z))
217.0ms	(* (* (* y (cbrt (- t z))) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t)))
164.0ms	(+ (* (* (* y (cbrt (- t z))) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) (+ y x))

series862.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(cbrt (- t z))
261.0ms	(cbrt (- t z))
122.0ms	(* (* (* y (cbrt (- t z))) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t)))
219.0ms	(+ (* (* (* y (cbrt (- t z))) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) (+ y x))

simplify1.7s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
1	1445
0	398

prune1.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 1.9b

regimes718.0ms

Accuracy

30.6% (5.9b remaining)

Error of 9.2b against oracle of 3.3b and baseline of 11.8b

bsearch111.0ms

Steps

Iters	Range		Point
8	1.2451536107620915e+24	1.7190669353889846e+27	1.6940211736100345e+27
6	-4.4705439518245044e+156	-2.9356007209192085e+155	-7.250982778284566e+155

simplify6.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample1.8s

Algorithm

intervals

Results

758.0ms	7311×	body	80	valid
123.0ms	263×	body	1280	valid
115.0ms	469×	body	640	valid
78.0ms	407×	body	320	valid
34.0ms	255×	body	160	valid
8.0ms	18×	body	2560	valid