Details

sample37.0ms

Algorithm

intervals

Results

17.0ms

268×

body

valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	1738
8	588
7	279
6	203
5	170
4	125
3	75
2	43
1	24
0	14

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(* z (- t a))
0.5b	(+ (* x y) (* z (- t a)))
21.1b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`prod-diff`
52×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+r+`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`sub-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 161

Calls

4 calls:

41.0ms	(* z (- b y))
37.0ms	(* z (- t a))
15.0ms	(+ (* x y) (* z (- t a)))
28.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series863.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* z (- b y))
51.0ms	(* z (- t a))
80.0ms	(+ (* x y) (* z (- t a)))
682.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify1.8s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
2	2864
1	710
0	291

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.2b

localize37.0ms

Local error

Found 3 expressions with local error:

0.5b	(fma (- t a) z (* x y))
0.6b	(/ 1 (/ (fma z (- b y) y) (fma (- t a) z (* x y))))
20.8b	(/ (fma z (- b y) y) (fma (- t a) z (* x y)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*` `add-exp-log`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`associate-/r/` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 117

Calls

3 calls:

0.0ms	(fma (- t a) z (* x y))
8.0ms	(/ 1 (/ (fma z (- b y) y) (fma (- t a) z (* x y))))
6.0ms	(/ (fma z (- b y) y) (fma (- t a) z (* x y)))

series901.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(fma (- t a) z (* x y))
686.0ms	(/ 1 (/ (fma z (- b y) y) (fma (- t a) z (* x y))))
142.0ms	(/ (fma z (- b y) y) (fma (- t a) z (* x y)))

simplify1.0s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1858
1	385
0	170

prune796.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.5b	(+ (* x y) (* z (- t a)))
0.7b	(/ 1 (fma z (- b y) y))
20.9b	(* (+ (* x y) (* z (- t a))) (/ 1 (fma z (- b y) y)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
46×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
20×	`times-frac`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `log1p-expm1-u` `unswap-sqr`
3×	`associate-/r` `flip3-+` `associate-r/` `cbrt-unprod` `flip-+` `associate-/l*`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `flip3--` `un-div-inv` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 157

Calls

4 calls:

30.0ms	(* z (- t a))
24.0ms	(+ (* x y) (* z (- t a)))
7.0ms	(/ 1 (fma z (- b y) y))
29.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (fma z (- b y) y)))

series682.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* z (- t a))
55.0ms	(+ (* x y) (* z (- t a)))
67.0ms	(/ 1 (fma z (- b y) y))
510.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (fma z (- b y) y)))

simplify2.0s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	3265
1	579
0	237

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 15.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- t a) z)
0.6b	(/ 1 (fma y x (* (- t a) z)))
0.6b	(/ 1 (* (fma z (- b y) y) (/ 1 (fma y x (* (- t a) z)))))
20.3b	(* (fma z (- b y) y) (/ 1 (fma y x (* (- t a) z))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
24×	`add-cube-cbrt`
23×	`times-frac`
22×	`add-cbrt-cube`
20×	`div-exp`
17×	`prod-exp`
16×	`associate-r`
12×	`pow1`
10×	`rec-exp` `1-exp`
8×	`associate-l`
6×	`cbrt-undiv` `associate-/l*`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `div-inv` `pow-flip`
2×	`clear-num` `frac-2neg` `associate-l/` `associate-r/` `associate-/r/` `un-div-inv` `*-commutative` `inv-pow`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 137

Calls

4 calls:

33.0ms	(* (- t a) z)
5.0ms	(/ 1 (fma y x (* (- t a) z)))
17.0ms	(/ 1 (* (fma z (- b y) y) (/ 1 (fma y x (* (- t a) z)))))
33.0ms	(* (fma z (- b y) y) (/ 1 (fma y x (* (- t a) z))))

series1.1s

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (- t a) z)
106.0ms	(/ 1 (fma y x (* (- t a) z)))
767.0ms	(/ 1 (* (fma z (- b y) y) (/ 1 (fma y x (* (- t a) z)))))
208.0ms	(* (fma z (- b y) y) (/ 1 (fma y x (* (- t a) z))))

simplify2.2s

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
2	2766
1	439
0	183

prune948.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 10.9b

regimes1.6s

Accuracy

69.5% (3.9b remaining)

Error of 15.1b against oracle of 11.3b and baseline of 24.0b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	43
3	43
2	40
1	37
0	29

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.3s

8428×

body

valid