Details

sample74.0ms

Algorithm

intervals

Results

28.0ms	222×	body	80	valid
5.0ms	13×	body	1280	valid
4.0ms	15×	body	640	valid
4.0ms	16×	body	320	valid
1.0ms	9×	body	160	valid

simplify13.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (80.0ms)

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: 12.4b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.2b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite35.0ms

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:

24.0ms	(/ (- t z) (- a t))
8.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series298.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- t z) (- a t))
242.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify1.5s

Counts

70 → 70

Iterations

Useful iterations: 3 (397.0ms)

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

prune254.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.2b	(* (/ (- t z) (- a t)) y)
2.2b	(+ (* (/ (- t z) (- a t)) y) (+ x y))

rewrite151.0ms

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:

35.0ms	(/ (- t z) (- a t))
71.0ms	(* (/ (- t z) (- a t)) y)
36.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

series470.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ (- t z) (- a t))
133.0ms	(* (/ (- t z) (- a t)) y)
274.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

simplify1.1s

Counts

133 → 133

Iterations

Useful iterations: done (1.1s)

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

prune394.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.5b	(+ (* (- t z) (/ y (- a t))) (+ x y))
9.1b	(* (- t z) (/ y (- a t)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 113

Calls

3 calls:

21.0ms	(/ y (- a t))
32.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
61.0ms	(* (- t z) (/ y (- a t)))

series311.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ y (- a t))
187.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
75.0ms	(* (- t z) (/ y (- a t)))

simplify1.7s

Counts

122 → 122

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	214	1838
1	635	1681
2	2750	1605
done	5000	1603

prune371.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
5.2b	(+ (* (- t z) (* y (/ 1 (- a t)))) (+ x y))
9.1b	(* (- t z) (* y (/ 1 (- a t))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-cbrt-cube`
16×	`associate-*r/` `frac-add`
13×	`prod-exp`
12×	`pow1` `frac-times`
11×	`flip3--` `flip--`
10×	`un-div-inv`
9×	`flip3-+` `flip-+` `add-log-exp`
8×	`associate-l` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `associate-*l/`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r/` `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 → 155

Calls

4 calls:

13.0ms	(/ 1 (- a t))
30.0ms	(* y (/ 1 (- a t)))
55.0ms	(+ (* (- t z) (* y (/ 1 (- a t)))) (+ x y))
57.0ms	(* (- t z) (* y (/ 1 (- a t))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (- a t))
43.0ms	(* y (/ 1 (- a t)))
157.0ms	(+ (* (- t z) (* y (/ 1 (- a t)))) (+ x y))
65.0ms	(* (- t z) (* y (/ 1 (- a t))))

simplify1.3s

Counts

167 → 167

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	254	2593
1	723	2102
2	2650	1958
done	5002	1956

prune388.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 3.4b

regimes422.0ms

Accuracy

40.9% (5.3b remaining)

Error of 8.3b against oracle of 3.0b and baseline of 11.9b

bsearch94.0ms

Steps

Iters	Range		Point
9	2.9580431597534113e+125	8.558334221433006e+131	1.5452334731429416e+127
8	-1.4169071298207385e+152	-4.961101422106634e+147	-8.502960241995041e+149

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	19	33
1	25	28
done	25	28

end0.0ms

sample1.4s

Algorithm

intervals

Results

556.0ms	7303×	body	80	valid
114.0ms	460×	body	640	valid
70.0ms	371×	body	320	valid
64.0ms	252×	body	1280	valid
61.0ms	282×	body	160	valid
6.0ms	21×	body	2560	valid