Details

sample43.0ms

Algorithm

intervals

Results

18.0ms

270×

body

valid

simplify6.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	14	17
1	24	16
2	43	15
3	75	15
4	112	15
5	148	15
6	181	15
7	257	15
8	419	15
9	728	15
10	1525	15
11	4096	15
done	5000	15

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
0.7b	(+ (* x y) (* z (- t a)))
23.7b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite163.0ms

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

Counts

4 → 161

Calls

4 calls:

27.0ms	(* z (- t a))
40.0ms	(* z (- b y))
35.0ms	(+ (* x y) (* z (- t a)))
42.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series778.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* z (- t a))
69.0ms	(* z (- b y))
103.0ms	(+ (* x y) (* z (- t a)))
544.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify1.4s

Counts

173 → 173

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	291	2904
1	619	2372
2	1671	1992
done	5000	1920

prune736.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.7b	(+ (* x y) (+ (* z t) (* z (- a))))
1.1b	(+ (* z t) (* z (- a)))
23.7b	(/ (+ (* x y) (+ (* z t) (* z (- a)))) (+ y (* z (- b y))))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

41.0ms	(* z (- b y))
44.0ms	(+ (* x y) (+ (* z t) (* z (- a))))
13.0ms	(+ (* z t) (* z (- a)))
116.0ms	(/ (+ (* x y) (+ (* z t) (* z (- a)))) (+ y (* z (- b y))))

series921.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* z (- b y))
117.0ms	(+ (* x y) (+ (* z t) (* z (- a))))
58.0ms	(+ (* z t) (* z (- a)))
670.0ms	(/ (+ (* x y) (+ (* z t) (* z (- a)))) (+ y (* z (- b y))))

simplify1.4s

Counts

128 → 128

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	215	2335
1	516	1779
2	1797	1550
done	5002	1524

prune480.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma t z (* x y))
2.2b	(/ a (/ (fma z (- b y) y) z))
13.9b	(/ (fma z (- b y) y) z)
21.0b	(/ (fma t z (* x y)) (fma z (- b y) y))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
62×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
7×	`div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`associate-/r/` `fma-udef`

Counts

4 → 140

Calls

4 calls:

1.0ms	(fma t z (* x y))
18.0ms	(/ a (/ (fma z (- b y) y) z))
6.0ms	(/ (fma z (- b y) y) z)
5.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

series871.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma t z (* x y))
93.0ms	(/ a (/ (fma z (- b y) y) z))
53.0ms	(/ (fma z (- b y) y) z)
667.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

simplify2.7s

Counts

152 → 152

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	217	2610
1	418	2522
2	1253	2356
3	3809	2354
done	5000	2354

prune869.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.5b	(fma t z (* x y))
2.2b	(/ a (- (+ (/ y z) b) y))
21.0b	(/ (fma t z (* x y)) (fma z (- b y) y))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
27×	`times-frac`
23×	`add-cube-cbrt`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp` `difference-of-squares`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/r/` `fma-udef` `div-inv`
1×	`flip3--` `flip--`

Counts

4 → 92

Calls

4 calls:

1.0ms	(fma z (- b y) y)
1.0ms	(fma t z (* x y))
123.0ms	(/ a (- (+ (/ y z) b) y))
18.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

series403.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma z (- b y) y)
74.0ms	(fma t z (* x y))
67.0ms	(/ a (- (+ (/ y z) b) y))
223.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

simplify1.4s

Counts

104 → 104

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	145	1507
1	265	1467
2	654	1349
3	1979	1349
done	5000	1349

prune579.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.9b

regimes707.0ms

Accuracy

-12.4% (7.1b remaining)

Error of 18.6b against oracle of 11.5b and baseline of 17.9b

bsearch241.0ms

Steps

Iters	Range	Point
9	1.331307691297302e-186	1.209597066017153e-181	1.4056232999710475e-186
6	-9.369023534978355e-298	-8.66213590632976e-299	-6.97840241981796e-298
9	-4.375475773243934e+160	-2.5035812315715853e+153	-6.665018424556654e+158

Iters

Range

Point

1.331307691297302e-186

1.209597066017153e-181

1.4056232999710475e-186

-9.369023534978355e-298

-8.66213590632976e-299

-6.97840241981796e-298

-4.375475773243934e+160

-2.5035812315715853e+153

-6.665018424556654e+158

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	94
1	40	94
done	40	94

end0.0ms

sample1.4s

Algorithm

intervals

Results

820.0ms

8404×

body

valid