Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	227×	body	80	valid
2.0ms	16×	body	1280	valid
2.0ms	16×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (30.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	51	13
3	103	13
4	205	12
5	409	12
6	666	12
7	973	12
8	1457	12
9	3545	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.1b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite15.0ms

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:

12.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series242.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (- t z) (- a t))
195.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify904.0ms

Counts

70 → 70

Iterations

Useful iterations: done (901.0ms)

Iter	Nodes	Cost
0	113	906
1	258	878
2	607	826
3	1863	824
done	5001	822

prune213.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* (- t z) (/ 1 (- a t)))
4.3b	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

rewrite34.0ms

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:

6.0ms	(/ 1 (- a t))
24.0ms	(* (- t z) (/ 1 (- a t)))
0.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

series277.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ 1 (- a t))
45.0ms	(* (- t z) (/ 1 (- a t)))
192.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

simplify1.7s

Counts

114 → 114

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	149	1273
1	335	1040
2	968	936
3	3194	934
done	5001	933

prune282.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.4b	(* (/ (- t z) (- a t)) y)
2.6b	(+ (* (/ (- t z) (- a t)) y) (+ x y))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 124

Calls

3 calls:

12.0ms	(/ (- t z) (- a t))
27.0ms	(* (/ (- t z) (- a t)) y)
14.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

series358.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (- t z) (- a t))
103.0ms	(* (/ (- t z) (- a t)) y)
208.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

simplify689.0ms

Counts

133 → 133

Iterations

Useful iterations: done (685.0ms)

Iter	Nodes	Cost
0	195	1736
1	543	1646
2	1569	1560
done	5000	1552

prune371.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(* (cbrt (- a t)) (cbrt (- a t)))
1.4b	(* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) y)
8.6b	(+ (* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) y) (+ x y))

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
36×	`prod-exp`
33×	`cbrt-prod`
32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cbrt-cube`
16×	`pow1` `cbrt-unprod`
15×	`div-exp`
14×	`add-cube-cbrt` `cbrt-div` `associate-*l/`
11×	`associate-r`
10×	`swap-sqr`
9×	`associate-l` `add-log-exp`
7×	`cbrt-undiv` `frac-times` `flip3--` `pow1/3` `flip--` `distribute-lft-out--`
6×	`frac-add`
5×	`associate-*r/` `pow-prod-down` `difference-of-squares`
4×	`expm1-log1p-u` `rec-exp` `flip3-+` `1-exp` `flip-+` `log1p-expm1-u` `unswap-sqr`
3×	`sum-log`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `pow2` `associate-+r+` `fma-def` `pow-plus`

Counts

4 → 138

Calls

4 calls:

2.0ms	(cbrt (- a t))
20.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
223.0ms	(* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) y)
225.0ms	(+ (* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) y) (+ x y))

series574.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt (- a t))
134.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
172.0ms	(* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) y)
107.0ms	(+ (* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))) y) (+ x y))

simplify1.2s

Counts

150 → 150

Iterations

Useful iterations: 2 (336.0ms)

Iter	Nodes	Cost
0	300	3225
1	857	2826
2	3284	2078
done	5001	2078

prune448.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.8b

regimes316.0ms

Accuracy

23% (6.2b remaining)

Error of 9.7b against oracle of 3.5b and baseline of 11.6b

bsearch87.0ms

Steps

Iters	Range		Point
6	5.548255359948423e+29	6.152553911645996e+30	5.6339865852383654e+29
9	-6.086858557591522e-81	-4.158131499047014e-90	-2.2439891650814672e-88

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	53
1	33	53
done	33	53

end0.0ms

sample667.0ms

Algorithm

intervals

Results

252.0ms	7343×	body	80	valid
55.0ms	461×	body	640	valid
39.0ms	260×	body	1280	valid
36.0ms	407×	body	320	valid
15.0ms	247×	body	160	valid
2.0ms	11×	body	2560	valid