Details

sample44.0ms

Algorithm

intervals

Results

16.0ms	236×	body	80	valid
3.0ms	19×	body	640	valid
3.0ms	11×	body	1280	valid
1.0ms	8×	body	320	valid
0.0ms	1×	body	160	valid

simplify13.4s

Counts

1 → 1

Iterations

Useful iterations: 4 (71.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	52	13
3	109	13
4	203	12
5	451	12
6	748	12
7	1078	12
8	1400	12
9	1655	12
10	2153	12
11	2683	12
12	3847	12
done	5001	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.0b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite37.0ms

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:

34.0ms	(/ (- t z) (- a t))
1.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series399.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/ (- t z) (- a t))
318.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify1.5s

Counts

70 → 70

Iterations

Useful iterations: 3 (515.0ms)

Iter	Nodes	Cost
0	113	906
1	258	878
2	622	826
3	1643	824
done	5000	824

prune281.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.7b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
0.8b	(+ (* (/ (- t z) (- a t)) y) (+ x y))
3.1b	(* (/ (- t z) (- a t)) y)

rewrite161.0ms

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:

40.0ms	(/ (- t z) (- a t))
42.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))
69.0ms	(* (/ (- t z) (- a t)) y)

series551.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(/ (- t z) (- a t))
309.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))
151.0ms	(* (/ (- t z) (- a t)) y)

simplify1.4s

Counts

133 → 133

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	195	1736
1	541	1646
2	1649	1560
done	5001	1549

prune457.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
3.1b	(* (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) y)
5.9b	(+ (* (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) y) (+ x y))

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
150×	`associate-l`
147×	`add-sqr-sqrt`
131×	`*-un-lft-identity`
120×	`cbrt-prod`
112×	`cbrt-div`
66×	`associate-/r/`
65×	`add-cube-cbrt`
56×	`flip3--` `flip--`
36×	`frac-times`
32×	`distribute-lft-out--`
30×	`difference-of-squares`
21×	`associate-*l/`
20×	`add-exp-log`
18×	`associate-*r/`
13×	`pow1` `add-cbrt-cube`
11×	`associate-r`
10×	`swap-sqr`
9×	`div-inv` `add-log-exp` `unswap-sqr`
7×	`pow1/3`
6×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `sum-log`
2×	`flip3-+` `frac-add` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+`
1×	`+-commutative` `pow2` `associate-+r+` `fma-def` `pow-plus`

Counts

4 → 263

Calls

4 calls:

6.0ms	(cbrt (- a t))
55.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
175.0ms	(* (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) y)
108.0ms	(+ (* (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) y) (+ x y))

series918.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(cbrt (- a t))
202.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
149.0ms	(* (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) y)
304.0ms	(+ (* (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) y) (+ x y))

simplify2.0s

Counts

275 → 275

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	398	5267
1	986	4926
2	3160	4291
done	5000	4076

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
0.9b	(pow (cbrt (cbrt (- a t))) (+ 3 1))
1.2b	(* (/ (/ (* (cbrt (- t z)) (cbrt (- t z))) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (* y (/ (cbrt (- t z)) (pow (cbrt (cbrt (- a t))) (+ 3 1)))))
7.4b	(+ (* (/ (/ (* (cbrt (- t z)) (cbrt (- t z))) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (* y (/ (cbrt (- t z)) (pow (cbrt (cbrt (- a t))) (+ 3 1))))) (+ x y))

rewrite655.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-exp-log`
88×	`times-frac`
76×	`associate-l`
75×	`cbrt-prod`
69×	`add-sqr-sqrt` `*-un-lft-identity`
43×	`add-cube-cbrt`
42×	`prod-exp`
40×	`cbrt-div`
37×	`div-exp`
33×	`add-cbrt-cube`
24×	`cbrt-unprod`
19×	`cbrt-undiv`
17×	`pow1`
16×	`flip3--` `associate-/r/` `flip--`
13×	`associate-*r/`
11×	`frac-times` `unpow-prod-down` `distribute-lft-out--`
10×	`swap-sqr`
9×	`associate-r` `add-log-exp` `difference-of-squares`
7×	`pow1/3` `associate-*l/`
6×	`frac-add`
5×	`pow-to-exp` `pow-prod-down` `pow-exp` `div-inv`
4×	`expm1-log1p-u` `pow-unpow` `flip3-+` `flip-+` `log1p-expm1-u` `unswap-sqr`
3×	`sum-log`
2×	`pow-pow` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`unpow-prod-up` `+-commutative` `pow2` `associate-+r+` `fma-def` `pow-plus` `distribute-lft-out` `sqr-pow`

Counts

4 → 226

Calls

4 calls:

53.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
23.0ms	(pow (cbrt (cbrt (- a t))) (+ 3 1))
314.0ms	(* (/ (/ (* (cbrt (- t z)) (cbrt (- t z))) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (* y (/ (cbrt (- t z)) (pow (cbrt (cbrt (- a t))) (+ 3 1)))))
247.0ms	(+ (* (/ (/ (* (cbrt (- t z)) (cbrt (- t z))) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (* y (/ (cbrt (- t z)) (pow (cbrt (cbrt (- a t))) (+ 3 1))))) (+ x y))

series1.1s

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
336.0ms	(pow (cbrt (cbrt (- a t))) (+ 3 1))
162.0ms	(* (/ (/ (* (cbrt (- t z)) (cbrt (- t z))) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (* y (/ (cbrt (- t z)) (pow (cbrt (cbrt (- a t))) (+ 3 1)))))
356.0ms	(+ (* (/ (/ (* (cbrt (- t z)) (cbrt (- t z))) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (* y (/ (cbrt (- t z)) (pow (cbrt (cbrt (- a t))) (+ 3 1))))) (+ x y))

simplify812.0ms

Counts

238 → 238

Iterations

Useful iterations: done (799.0ms)

Iter	Nodes	Cost
0	447	8191
1	1284	7280
done	5001	6085

prune2.0s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 3.7b

regimes478.0ms

Accuracy

14.1% (6.6b remaining)

Error of 9.6b against oracle of 3.0b and baseline of 10.7b

bsearch148.0ms

Steps

Iters	Range		Point
9	2.9088581115424155e-25	7.432584257913239e-20	1.5633799213363547e-22
10	-1.2606852365757149e-221	-8.95343244323789e-237	-2.0739807261178848e-225

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	20	41
1	28	29
done	28	29

end0.0ms

sample1.5s

Algorithm

intervals

Results

555.0ms	7343×	body	80	valid
108.0ms	231×	body	1280	valid
92.0ms	405×	body	320	valid
90.0ms	454×	body	640	valid
38.0ms	16×	body	2560	valid
29.0ms	244×	body	160	valid