Details

sample74.0ms

Algorithm

intervals

Results

29.0ms	231×	body	80	valid
8.0ms	17×	body	640	valid
7.0ms	11×	body	1280	valid
5.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
8	3757
7	2046
6	989
5	406
4	195
3	103
2	50
1	22
0	11

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.3b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
13.3b	(fma (- t z) (/ y (- a t)) (+ x y))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `fma-udef` `div-inv` `flip--`

Counts

2 → 51

Calls

2 calls:

17.0ms	(/ y (- a t))
1.0ms	(fma (- t z) (/ y (- a t)) (+ x y))

series208.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ y (- a t))
162.0ms	(fma (- t z) (/ y (- a t)) (+ x y))

simplify1.3s

Counts

57 → 57

Iterations

Iter	Nodes
done	5000
3	1386
2	456
1	176
0	94

prune419.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
13.3b	(fma (- t z) (* y (/ 1 (- a t))) (+ x y))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `cbrt-unprod` `div-inv` `flip--`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 102

Calls

3 calls:

10.0ms	(/ 1 (- a t))
26.0ms	(* y (/ 1 (- a t)))
0.0ms	(fma (- t z) (* y (/ 1 (- a t))) (+ x y))

series260.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ 1 (- a t))
37.0ms	(* y (/ 1 (- a t)))
149.0ms	(fma (- t z) (* y (/ 1 (- a t))) (+ x y))

simplify1.9s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
3	1934
2	768
1	299
0	135

prune543.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
4.4b	(+ (* (- t z) (/ y (- a t))) (+ x y))
9.6b	(* (- t z) (/ y (- a t)))

rewrite102.0ms

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-cbrt-cube` `frac-add` `add-exp-log`
8×	`flip3--` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`frac-times` `flip3-+` `associate-*l/` `flip-+`
5×	`pow1` `associate-/r` `associate-l*`
4×	`associate-/r/`
3×	`expm1-log1p-u` `sum-log` `associate-r/` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `clear-num` `fma-def` `frac-2neg` `pow-prod-down` `*-commutative`

Counts

3 → 116

Calls

3 calls:

14.0ms	(/ y (- a t))
45.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
41.0ms	(* (- t z) (/ y (- a t)))

series355.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ y (- a t))
209.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
100.0ms	(* (- t z) (/ y (- a t)))

simplify2.5s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
2	3040
1	675
0	217

prune853.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
3.3b	(* (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
8.1b	(+ (* (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))) (+ x y))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`associate-/r/`
9×	`flip3--` `flip--` `add-log-exp`
8×	`prod-exp` `cbrt-unprod`
7×	`frac-times` `cbrt-undiv` `div-exp`
6×	`pow1` `frac-add` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
5×	`associate-l/` `associate-r/`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`sum-log`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `associate-+r+` `fma-def` `pow-prod-down` `*-commutative`

Counts

4 → 139

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
114.0ms	(* (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
65.0ms	(+ (* (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))) (+ x y))

series932.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(cbrt (- a t))
217.0ms	(cbrt (- a t))
166.0ms	(* (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
321.0ms	(+ (* (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))) (+ x y))

simplify2.6s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
2	3540
1	889
0	282

prune772.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 4.2b

regimes684.0ms

Accuracy

26.6% (6.0b remaining)

Error of 9.2b against oracle of 3.2b and baseline of 11.4b

bsearch108.0ms

Steps

Iters	Range		Point
9	5.0875015420834634e-30	1.4423693549975343e-20	5.959771805378206e-30
7	-1.062177424076527e-128	-3.4706779128300513e-130	-4.3730723253157225e-129

simplify6.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample1.6s

Algorithm

intervals

Results

796.0ms	7368×	body	80	valid
187.0ms	260×	body	1280	valid
167.0ms	434×	body	640	valid
100.0ms	400×	body	320	valid
46.0ms	259×	body	160	valid
5.0ms	10×	body	2560	valid