Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	246×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	7×	body	1280	valid
1.0ms	11×	body	160	valid

simplify9.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (12.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	114	12
4	278	12
5	618	12
6	1256	12
7	2316	12
8	4161	12
done	5001	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
13.2b	(fma (/ (- y x) (- a t)) (- z t) x)

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

series138.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- y x) (- a t))
85.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.9s

Counts

70 → 70

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	118	918
1	270	890
2	628	838
3	1591	836
4	4648	828
done	5000	828

prune220.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.5b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
5.1b	(* (/ (- y x) (- a t)) (- z t))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

13.0ms	(/ (- y x) (- a t))
15.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
37.0ms	(* (/ (- y x) (- a t)) (- z t))

series390.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- y x) (- a t))
137.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
199.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify1.1s

Counts

179 → 179

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	256	3107
1	682	2740
2	2109	2516
done	5001	2480

prune465.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.8b	(+ (* (- y x) (/ (- z t) (- a t))) x)
3.0b	(* (- y x) (/ (- z t) (- a t)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

12.0ms	(/ (- z t) (- a t))
12.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)
36.0ms	(* (- y x) (/ (- z t) (- a t)))

series319.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ (- z t) (- a t))
152.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)
118.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify1.0s

Counts

135 → 135

Iterations

Useful iterations: 2 (276.0ms)

Iter	Nodes	Cost
0	189	1881
1	492	1765
2	1727	1669
done	5000	1669

prune370.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- z t) (/ 1 (- a t)))
3.0b	(* (- y x) (* (- z t) (/ 1 (- a t))))
3.3b	(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 155

Calls

4 calls:

6.0ms	(/ 1 (- a t))
27.0ms	(* (- z t) (/ 1 (- a t)))
35.0ms	(* (- y x) (* (- z t) (/ 1 (- a t))))
30.0ms	(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

series358.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1 (- a t))
48.0ms	(* (- z t) (/ 1 (- a t)))
116.0ms	(* (- y x) (* (- z t) (/ 1 (- a t))))
156.0ms	(+ (* (- y x) (* (- z t) (/ 1 (- a t)))) x)

simplify1.1s

Counts

167 → 167

Iterations

Useful iterations: 2 (335.0ms)

Iter	Nodes	Cost
0	229	2378
1	605	2004
2	2211	1782
done	5000	1782

prune390.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

regimes287.0ms

Accuracy

5.1% (7.2b remaining)

Error of 11.3b against oracle of 4.2b and baseline of 11.7b

bsearch147.0ms

Steps

Iters	Range	Point
8	1.334149254675946e+295	4.067056781871996e+298	4.0194876181204073e+298
8	2.113839912867758e+227	2.4112655861716263e+231	2.1292815435723623e+229
8	-1.1995038685743404e+237	-2.1909922675420783e+232	-1.1745291012592303e+237

Iters

Range

Point

1.334149254675946e+295

4.067056781871996e+298

4.0194876181204073e+298

2.113839912867758e+227

2.4112655861716263e+231

2.1292815435723623e+229

-1.1995038685743404e+237

-2.1909922675420783e+232

-1.1745291012592303e+237

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	79
1	37	79
done	37	79

end1.0ms

sample706.0ms

Algorithm

intervals

Results

259.0ms	7781×	body	80	valid
62.0ms	465×	body	640	valid
45.0ms	278×	body	1280	valid
37.0ms	416×	body	320	valid
17.0ms	271×	body	160	valid
4.0ms	20×	body	2560	valid