Details

sample54.0ms

Algorithm

intervals

Results

16.0ms	247×	body	80	valid
6.0ms	25×	body	640	valid
3.0ms	17×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	10×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3874
5	979
4	326
3	116
2	45
1	20
0	11

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.2b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- a t))
4.1b	(fma (/ (- z t) (- a t)) (- y x) x)

rewrite30.0ms

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-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

27.0ms	(/ (- z t) (- a t))
0.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

series238.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/ (- z t) (- a t))
181.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

simplify2.1s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4602
2	861
1	272
0	116

prune474.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.1b	(* (/ (- z t) (- a t)) (- y x))
3.3b	(+ (* (/ (- z t) (- a t)) (- y x)) x)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

24.0ms	(/ (- z t) (- a t))
54.0ms	(* (/ (- z t) (- a t)) (- y x))
23.0ms	(+ (* (/ (- z t) (- a t)) (- y x)) x)

series695.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- z t) (- a t))
382.0ms	(* (/ (- z t) (- a t)) (- y x))
238.0ms	(+ (* (/ (- z t) (- a t)) (- y x)) x)

simplify1.8s

Counts

179 → 179

Iterations

Iter	Nodes
done	5001
2	3220
1	717
0	255

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.4b	(/ 1 (/ (- a t) (- z t)))
2.1b	(* (/ 1 (/ (- a t) (- z t))) (- y x))
3.3b	(+ (* (/ 1 (/ (- a t) (- z t))) (- y x)) x)

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
362×	`add-sqr-sqrt`
350×	`*-un-lft-identity`
182×	`add-cube-cbrt`
98×	`associate-l`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*` `prod-diff` `add-exp-log`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-r` `unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `sub-neg` `1-exp` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*r/` `associate-/l/`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 396

Calls

4 calls:

28.0ms	(/ (- a t) (- z t))
40.0ms	(/ 1 (/ (- a t) (- z t)))
102.0ms	(* (/ 1 (/ (- a t) (- z t))) (- y x))
34.0ms	(+ (* (/ 1 (/ (- a t) (- z t))) (- y x)) x)

series961.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (- a t) (- z t))
184.0ms	(/ 1 (/ (- a t) (- z t)))
441.0ms	(* (/ 1 (/ (- a t) (- z t))) (- y x))
277.0ms	(+ (* (/ 1 (/ (- a t) (- z t))) (- y x)) x)

simplify1.2s

Counts

408 → 408

Iterations

Iter	Nodes
done	5001
1	1389
0	463

prune2.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- z t))
0.5b	(cbrt (- z t))
0.5b	(cbrt (- z t))
11.7b	(fma (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))) (- y x) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

6.0ms	(cbrt (- z t))
6.0ms	(cbrt (- z t))
6.0ms	(cbrt (- z t))
1.0ms	(fma (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))) (- y x) x)

series765.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(cbrt (- z t))
218.0ms	(cbrt (- z t))
172.0ms	(cbrt (- z t))
153.0ms	(fma (* (* (cbrt (- z t)) (cbrt (- z t))) (/ (cbrt (- z t)) (- a t))) (- y x) x)

simplify1.5s

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
3	1782
2	510
1	199
0	96

prune498.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 5.1b

regimes1.2s

Accuracy

31.5% (5.8b remaining)

Error of 9.0b against oracle of 3.2b and baseline of 11.6b

bsearch164.0ms

Steps

Iters	Range		Point
10	5.2644298199866365e-157	2.7232975322406408e-140	4.822059143857127e-150
8	-2.539644303582551e-91	-1.7804719413044463e-94	-1.9039405874823513e-94

simplify7.0ms

Iterations

Iter	Nodes
done	32
1	32
0	23

end0.0ms

sample1.4s

Algorithm

intervals

Results

718.0ms	7837×	body	80	valid
122.0ms	504×	body	640	valid
96.0ms	404×	body	320	valid
71.0ms	266×	body	1280	valid
25.0ms	242×	body	160	valid
3.0ms	11×	body	2560	valid