Details

sample48.0ms

Algorithm

intervals

Results

13.0ms	234×	body	80	valid
3.0ms	16×	body	640	valid
3.0ms	12×	body	1280	valid
3.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	1×	body	2560	valid

simplify12.7s

Counts

1 → 1

Iterations

Useful iterations: 4 (63.0ms)

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite58.0ms

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:

52.0ms	(/ (- t z) (- a t))
1.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series490.0ms

Counts

2 → 6

Calls

2 calls:

101.0ms	(/ (- t z) (- a t))
388.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify2.0s

Counts

70 → 70

Iterations

Useful iterations: 3 (875.0ms)

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

prune326.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.3b	(* (/ (- t z) (- a t)) y)
2.9b	(+ (* (/ (- t z) (- a t)) y) (+ x y))

rewrite193.0ms

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:

51.0ms	(/ (- t z) (- a t))
79.0ms	(* (/ (- t z) (- a t)) y)
53.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

series522.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (- t z) (- a t))
144.0ms	(* (/ (- t z) (- a t)) y)
306.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

simplify1.5s

Counts

133 → 133

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	195	1736
1	541	1646
2	1652	1560
done	5001	1549

prune556.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
1.3b	(* (* (- t z) (/ 1 (- a t))) y)
5.3b	(+ (* (* (- t z) (/ 1 (- a t))) y) (+ x y))

rewrite460.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
26×	`associate-*l/`
25×	`add-cube-cbrt`
24×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1` `frac-add`
10×	`flip3--` `flip--`
9×	`add-log-exp`
8×	`frac-times` `distribute-lft-out--` `difference-of-squares`
7×	`flip3-+` `cbrt-unprod` `flip-+`
6×	`div-exp` `associate-l`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `associate-/r/` `un-div-inv` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `1-exp` `sum-log` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `associate-+r+` `pow-flip` `fma-def` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 153

Calls

4 calls:

28.0ms	(/ 1 (- a t))
105.0ms	(* (- t z) (/ 1 (- a t)))
146.0ms	(* (* (- t z) (/ 1 (- a t))) y)
167.0ms	(+ (* (* (- t z) (/ 1 (- a t))) y) (+ x y))

series696.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ 1 (- a t))
72.0ms	(* (- t z) (/ 1 (- a t)))
181.0ms	(* (* (- t z) (/ 1 (- a t))) y)
384.0ms	(+ (* (* (- t z) (/ 1 (- a t))) y) (+ x y))

simplify2.3s

Counts

165 → 165

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	251	2482
1	725	2016
2	2885	1854
done	5002	1852

prune679.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize30.0ms

Local error

Found 4 expressions with local error:

2.9b	(+ (* (* (* (cbrt (/ (- t z) (- a t))) (cbrt (/ (- t z) (- a t)))) (cbrt (/ (- t z) (- a t)))) y) (+ x y))
3.4b	(cbrt (/ (- t z) (- a t)))
3.4b	(cbrt (/ (- t z) (- a t)))
3.4b	(cbrt (/ (- t z) (- a t)))

rewrite727.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
27×	`cbrt-div`
24×	`associate-*l/`
14×	`frac-add`
10×	`frac-times`
9×	`add-log-exp`
8×	`flip3-+` `flip-+`
6×	`associate-*r/` `associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `pow1/3` `sum-log` `flip--` `div-inv`
1×	`+-commutative` `associate-+r+` `fma-def`

Counts

4 → 156

Calls

4 calls:

661.0ms	(+ (* (* (* (cbrt (/ (- t z) (- a t))) (cbrt (/ (- t z) (- a t)))) (cbrt (/ (- t z) (- a t)))) y) (+ x y))
22.0ms	(cbrt (/ (- t z) (- a t)))
11.0ms	(cbrt (/ (- t z) (- a t)))
18.0ms	(cbrt (/ (- t z) (- a t)))

series1.8s

Counts

4 → 12

Calls

4 calls:

355.0ms	(+ (* (* (* (cbrt (/ (- t z) (- a t))) (cbrt (/ (- t z) (- a t)))) (cbrt (/ (- t z) (- a t)))) y) (+ x y))
443.0ms	(cbrt (/ (- t z) (- a t)))
484.0ms	(cbrt (/ (- t z) (- a t)))
489.0ms	(cbrt (/ (- t z) (- a t)))

simplify1.6s

Counts

168 → 168

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	225	3785
1	596	3615
2	1740	3137
done	5001	3016

prune885.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.2b

regimes607.0ms

Accuracy

6.1% (5.3b remaining)

Error of 8.8b against oracle of 3.5b and baseline of 9.2b

bsearch196.0ms

Steps

Iters	Range		Point
8	9.740644972667289e-27	7.715974239653845e-24	1.1325476279686525e-26
8	-2.0516827023024987e-114	-3.3467573401782356e-118	-2.3225014648936276e-115

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	21	96
1	26	56
done	26	56

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	7307×	body	80	valid
124.0ms	403×	body	320	valid
114.0ms	470×	body	640	valid
81.0ms	276×	body	1280	valid
33.0ms	272×	body	160	valid
7.0ms	15×	body	2560	valid