Details

sample27.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 4 (47.0ms)

Iter	Nodes	Cost
0	16	21
1	33	20
2	78	20
3	154	20
4	371	19
5	707	19
6	1188	19
7	2414	19
done	5000	19

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.3b	(+ (* (+ x y) z) (* (+ t y) a))
2.8b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.8b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

10.0ms	(* (+ x y) z)
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
41.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
84.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series785.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ x y) z)
53.0ms	(+ (* (+ x y) z) (* (+ t y) a))
104.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
606.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify749.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	194	2540
1	586	2317
2	2378	2102
done	5001	2102

prune592.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma t a (* y (- a b))))))
0.5b	(fma t a (* y (- a b)))
1.3b	(fma z (+ x y) (fma t a (* y (- a b))))
24.9b	(/ (+ (+ x t) y) (fma z (+ x y) (fma t a (* y (- a b)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
132×	`times-frac`
70×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
22×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef` `associate-/l/`
1×	`pow-flip` `flip3-+` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 161

Calls

4 calls:

22.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma t a (* y (- a b))))))
0.0ms	(fma t a (* y (- a b)))
0.0ms	(fma z (+ x y) (fma t a (* y (- a b))))
34.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (fma t a (* y (- a b)))))

series822.0ms

Counts

4 → 12

Calls

4 calls:

581.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma t a (* y (- a b))))))
33.0ms	(fma t a (* y (- a b)))
101.0ms	(fma z (+ x y) (fma t a (* y (- a b))))
107.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (fma t a (* y (- a b)))))

simplify1.1s

Counts

173 → 173

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	190	5188
1	432	4893
2	1501	4452
done	5001	4421

prune380.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (+ (* z (+ x y)) (fma t a (* y (- a b))))))
0.5b	(fma t a (* y (- a b)))
2.2b	(+ (* z (+ x y)) (fma t a (* y (- a b))))
24.9b	(/ (+ (+ x t) y) (+ (* z (+ x y)) (fma t a (* y (- a b)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

152×	`*-un-lft-identity`
138×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
24×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `associate-+l+` `frac-2neg` `1-exp` `clear-num` `fma-udef` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `associate-+r+` `pow-flip` `fma-def` `distribute-lft-in` `sum-log` `inv-pow`

Counts

4 → 178

Calls

4 calls:

31.0ms	(/ 1 (/ (+ (+ x t) y) (+ (* z (+ x y)) (fma t a (* y (- a b))))))
0.0ms	(fma t a (* y (- a b)))
5.0ms	(+ (* z (+ x y)) (fma t a (* y (- a b))))
40.0ms	(/ (+ (+ x t) y) (+ (* z (+ x y)) (fma t a (* y (- a b)))))

series804.0ms

Counts

4 → 12

Calls

4 calls:

574.0ms	(/ 1 (/ (+ (+ x t) y) (+ (* z (+ x y)) (fma t a (* y (- a b))))))
32.0ms	(fma t a (* y (- a b)))
97.0ms	(+ (* z (+ x y)) (fma t a (* y (- a b))))
102.0ms	(/ (+ (+ x t) y) (+ (* z (+ x y)) (fma t a (* y (- a b)))))

simplify1.1s

Counts

190 → 190

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	221	6078
1	534	5476
2	1938	5039
done	5001	5038

prune409.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
0.5b	(fma t a (* y (- a b)))
1.3b	(fma (+ x y) z (fma t a (* y (- a b))))
24.9b	(* (/ 1 (+ (+ x t) y)) (fma (+ x y) z (fma t a (* y (- a b)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
32×	`times-frac`
31×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
21×	`associate-l` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`distribute-rgt-in` `pow-flip` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `inv-pow`

Counts

4 → 110

Calls

4 calls:

18.0ms	(/ 1 (+ (+ x t) y))
0.0ms	(fma t a (* y (- a b)))
0.0ms	(fma (+ x y) z (fma t a (* y (- a b))))
44.0ms	(* (/ 1 (+ (+ x t) y)) (fma (+ x y) z (fma t a (* y (- a b)))))

series759.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (+ (+ x t) y))
31.0ms	(fma t a (* y (- a b)))
99.0ms	(fma (+ x y) z (fma t a (* y (- a b))))
573.0ms	(* (/ 1 (+ (+ x t) y)) (fma (+ x y) z (fma t a (* y (- a b)))))

simplify2.2s

Counts

122 → 122

Iterations

Useful iterations: 3 (581.0ms)

Iter	Nodes	Cost
0	140	2083
1	328	1931
2	1107	1689
3	4457	1687
done	5000	1687

prune292.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.1b

regimes679.0ms

Accuracy

46.6% (11.7b remaining)

Error of 16.2b against oracle of 4.4b and baseline of 26.4b

bsearch74.0ms

Steps

Iters	Range		Point
8	2.4068838490227673e+40	1.0542243044934032e+43	1.2918166468940466e+42
5	-6.289516594595149e+115	-1.85370030410588e+115	-1.880087478392796e+115

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	25	42
1	35	36
done	35	36

end0.0ms

sample605.0ms

Algorithm

intervals

Results

339.0ms

8000×

body

valid