Details

sample47.0ms

Algorithm

intervals

Results

16.0ms	249×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	7×	body	1280	valid
1.0ms	9×	body	160	valid
0.0ms	1×	body	2560	valid

simplify2.9s

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.6b

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- a t))
3.9b	(fma (/ (- z t) (- a t)) (- y x) x)

rewrite42.0ms

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:

38.0ms	(/ (- z t) (- a t))
1.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

series241.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- z t) (- a t))
182.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

simplify1.8s

Counts

70 → 70

Iterations

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

prune571.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.4b	(/ 1 (/ (- a t) (- z t)))
3.9b	(fma (/ 1 (/ (- a t) (- z t))) (- y x) x)

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `div-inv` `flip--`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`div-sub` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 214

Calls

3 calls:

47.0ms	(/ (- a t) (- z t))
36.0ms	(/ 1 (/ (- a t) (- z t)))
0.0ms	(fma (/ 1 (/ (- a t) (- z t))) (- y x) x)

series497.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(/ (- a t) (- z t))
201.0ms	(/ 1 (/ (- a t) (- z t)))
227.0ms	(fma (/ 1 (/ (- a t) (- z t))) (- y x) x)

simplify1.5s

Counts

223 → 223

Iterations

Iter	Nodes
done	5002
2	3962
1	714
0	273

prune845.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- z t))
0.2b	(* (- a t) (/ 1 (- z t)))
0.4b	(/ 1 (* (- a t) (/ 1 (- z t))))
4.4b	(fma (/ 1 (* (- a t) (/ 1 (- z t)))) (- y x) x)

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-cbrt-cube` `div-exp`
16×	`prod-exp`
10×	`pow1` `rec-exp` `1-exp` `associate-/r/`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `associate-/r` `flip3--` `flip--` `associate-/l`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `pow-flip` `unswap-sqr`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*r/` `un-div-inv` `inv-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 151

Calls

4 calls:

17.0ms	(/ 1 (- z t))
61.0ms	(* (- a t) (/ 1 (- z t)))
37.0ms	(/ 1 (* (- a t) (/ 1 (- z t))))
0.0ms	(fma (/ 1 (* (- a t) (/ 1 (- z t)))) (- y x) x)

series500.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (- z t))
55.0ms	(* (- a t) (/ 1 (- z t)))
168.0ms	(/ 1 (* (- a t) (/ 1 (- z t))))
226.0ms	(fma (/ 1 (* (- a t) (/ 1 (- z t)))) (- y x) x)

simplify4.6s

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
2	3817
1	498
0	196

prune887.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.1b

localize25.0ms

Local error

Found 4 expressions with local error:

3.9b	(fma (* (/ (/ 1 (cbrt (/ (- a t) (- z t)))) (cbrt (/ (- a t) (- z t)))) (/ 1 (cbrt (/ (- a t) (- z t))))) (- y x) x)
4.7b	(cbrt (/ (- a t) (- z t)))
4.7b	(cbrt (/ (- a t) (- z t)))
4.7b	(cbrt (/ (- a t) (- z t)))

rewrite39.0ms

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`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `div-inv` `flip--`
1×	`fma-udef`

Counts

4 → 136

Calls

4 calls:

0.0ms	(fma (* (/ (/ 1 (cbrt (/ (- a t) (- z t)))) (cbrt (/ (- a t) (- z t)))) (/ 1 (cbrt (/ (- a t) (- z t))))) (- y x) x)
8.0ms	(cbrt (/ (- a t) (- z t)))
9.0ms	(cbrt (/ (- a t) (- z t)))
16.0ms	(cbrt (/ (- a t) (- z t)))

series1.4s

Counts

4 → 12

Calls

4 calls:

163.0ms	(fma (* (/ (/ 1 (cbrt (/ (- a t) (- z t)))) (cbrt (/ (- a t) (- z t)))) (/ 1 (cbrt (/ (- a t) (- z t))))) (- y x) x)
450.0ms	(cbrt (/ (- a t) (- z t)))
386.0ms	(cbrt (/ (- a t) (- z t)))
433.0ms	(cbrt (/ (- a t) (- z t)))

simplify1.6s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
3	2910
2	782
1	350
0	181

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.1b

regimes1.1s

Accuracy

44.3% (4.5b remaining)

Error of 8.4b against oracle of 4.0b and baseline of 12.0b

bsearch3.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	42
1	42
0	33

end0.0ms

sample2.1s

Algorithm

intervals

Results

589.0ms	500×	body	640	valid
548.0ms	7765×	body	80	valid
115.0ms	276×	body	1280	valid
113.0ms	422×	body	320	valid
103.0ms	282×	body	160	valid
2.0ms	5×	body	2560	valid