Details

sample42.0ms

Algorithm

intervals

Results

16.0ms	228×	body	80	valid
5.0ms	18×	body	640	valid
4.0ms	20×	body	320	valid
3.0ms	8×	body	1280	valid
1.0ms	10×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3465
5	879
4	292
3	111
2	45
1	20
0	11

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.0b	(+ x (/ (* (- y x) (- z t)) (- a t)))
19.4b	(/ (* (- y x) (- z t)) (- a t))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-cbrt-cube` `add-exp-log`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `associate-/r` `times-frac` `associate-r` `associate-l*` `add-log-exp`
4×	`associate-l/` `associate-r/` `distribute-lft-out--` `difference-of-squares`
3×	`insert-posit16`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `pow-prod-down` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

25.0ms	(* (- y x) (- z t))
13.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
22.0ms	(/ (* (- y x) (- z t)) (- a t))

series425.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* (- y x) (- z t))
244.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
129.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify1.6s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	2662
1	483
0	165

prune479.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub` `insert-posit16`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+r-` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

3 → 277

Calls

3 calls:

15.0ms	(/ (- a t) (- z t))
26.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
24.0ms	(/ (- y x) (/ (- a t) (- z t)))

series554.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (- a t) (- z t))
234.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
262.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify1.0s

Counts

286 → 286

Iterations

Iter	Nodes
done	5001
1	1157
0	357

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.3b	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
2.1b	(/ (/ (- a t) (- z t)) (- y x))
3.9b	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

1933×	`times-frac`
1483×	`*-un-lft-identity`
1480×	`add-sqr-sqrt`
624×	`add-cube-cbrt`
428×	`distribute-lft-out--` `difference-of-squares`
171×	`associate-/r*`
65×	`associate-/r/`
39×	`associate-/l*`
34×	`div-inv`
33×	`flip3--` `flip--`
32×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`div-exp`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`insert-posit16`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `div-sub` `associate-/l/`
2×	`distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 950

Calls

4 calls:

17.0ms	(/ (- a t) (- z t))
35.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
42.0ms	(/ (/ (- a t) (- z t)) (- y x))
50.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

series828.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (- a t) (- z t))
356.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
178.0ms	(/ (/ (- a t) (- z t)) (- y x))
238.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

simplify2.5s

Counts

962 → 962

Iterations

Iter	Nodes
done	5002
1	2730
0	932

prune3.6s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ t (- z t))
0.3b	(/ 1 (/ (- (/ a (- z t)) (/ t (- z t))) (- y x)))
2.1b	(/ (- (/ a (- z t)) (/ t (- z t))) (- y x))
3.9b	(+ x (/ 1 (/ (- (/ a (- z t)) (/ t (- z t))) (- y x))))

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

1221×	`times-frac`
1153×	`*-un-lft-identity`
890×	`add-sqr-sqrt`
407×	`distribute-lft-out--`
284×	`add-cube-cbrt`
251×	`difference-of-squares`
117×	`associate-/r/`
106×	`associate-/r*`
78×	`distribute-rgt-out--`
60×	`div-inv`
59×	`flip3--` `flip--`
24×	`associate-/l*`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`div-exp`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
2×	`rec-exp` `1-exp` `distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `div-sub` `frac-sub` `flip-+` `pow-flip` `inv-pow` `sub-div`

Counts

4 → 594

Calls

4 calls:

11.0ms	(/ t (- z t))
99.0ms	(/ 1 (/ (- (/ a (- z t)) (/ t (- z t))) (- y x)))
113.0ms	(/ (- (/ a (- z t)) (/ t (- z t))) (- y x))
89.0ms	(+ x (/ 1 (/ (- (/ a (- z t)) (/ t (- z t))) (- y x))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ t (- z t))
350.0ms	(/ 1 (/ (- (/ a (- z t)) (/ t (- z t))) (- y x)))
132.0ms	(/ (- (/ a (- z t)) (/ t (- z t))) (- y x))
199.0ms	(+ x (/ 1 (/ (- (/ a (- z t)) (/ t (- z t))) (- y x))))

simplify1.8s

Counts

606 → 606

Iterations

Iter	Nodes
done	5001
1	1912
0	680

prune2.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.7b

regimes830.0ms

Accuracy

13.3% (6.2b remaining)

Error of 10.4b against oracle of 4.2b and baseline of 11.3b

bsearch189.0ms

Steps

Iters	Range		Point
6	1.0855991885052202e-135	5.806846775016059e-135	1.0989115963069107e-135
10	-3.7853197546515783e-110	-1.648318488097239e-120	-1.4427683470607565e-114

simplify9.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample1.8s

Algorithm

intervals

Results

998.0ms	7793×	body	80	valid
171.0ms	471×	body	640	valid
140.0ms	261×	body	1280	valid
136.0ms	414×	body	320	valid
41.0ms	241×	body	160	valid
3.0ms	8×	body	2560	valid