Details

sample42.0ms

Algorithm

intervals

Results

21.0ms

265×

body

valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	24	16
2	43	15
3	75	15
4	127	15
5	182	15
6	215	15
7	291	15
8	600	15
9	1748	15
done	5000	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
23.5b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-r`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`sub-neg` `associate-*r/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 85

Calls

3 calls:

25.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
5.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series500.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* z (- t a))
57.0ms	(fma x y (* z (- t a)))
404.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify521.0ms

Counts

94 → 94

Iterations

Useful iterations: done (519.0ms)

Iter	Nodes	Cost
0	163	1562
1	337	1384
2	1097	1192
done	5001	1164

prune306.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.2b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.3b	(fma x y (* z (- t a)))
23.5b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
72×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
68×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`prod-diff`
16×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`div-exp`
7×	`pow1`
6×	`div-inv` `associate-/l*`
5×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`sub-neg` `rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num`
1×	`flip3--` `pow-flip` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 163

Calls

4 calls:

34.0ms	(* z (- t a))
13.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.0ms	(fma x y (* z (- t a)))
8.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series842.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* z (- t a))
576.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
58.0ms	(fma x y (* z (- t a)))
148.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify1.4s

Counts

175 → 175

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	264	3896
1	599	3513
2	2447	3184
done	5001	3080

prune574.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
0.7b	(/ 1 (fma z (- b y) y))
23.4b	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
18×	`prod-diff`
16×	`associate-l`
13×	`add-cbrt-cube`
12×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`associate-r`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `cbrt-unprod` `fma-udef` `associate-/l`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `div-inv`
1×	`flip3--` `pow-flip` `frac-2neg` `associate-*l/` `clear-num` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 128

Calls

4 calls:

30.0ms	(* z (- t a))
1.0ms	(fma x y (* z (- t a)))
10.0ms	(/ 1 (fma z (- b y) y))
32.0ms	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

series752.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* z (- t a))
60.0ms	(fma x y (* z (- t a)))
63.0ms	(/ 1 (fma z (- b y) y))
579.0ms	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

simplify1.0s

Counts

140 → 140

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	207	2186
1	471	1894
2	2102	1616
done	5002	1586

prune417.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.5b

localize27.0ms

Local error

Found 2 expressions with local error:

0.5b	(fma (- t a) z (* y x))
23.5b	(/ (fma (- t a) z (* y x)) (fma z (- b y) y))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma (- t a) z (* y x))
9.0ms	(/ (fma (- t a) z (* y x)) (fma z (- b y) y))

series442.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(fma (- t a) z (* y x))
385.0ms	(/ (fma (- t a) z (* y x)) (fma z (- b y) y))

simplify898.0ms

Counts

45 → 45

Iterations

Useful iterations: 3 (161.0ms)

Iter	Nodes	Cost
0	70	843
1	118	832
2	296	754
3	1057	752
done	5001	752

prune280.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 9.5b

regimes561.0ms

Accuracy

26.8% (10.7b remaining)

Error of 19.5b against oracle of 8.8b and baseline of 23.4b

bsearch164.0ms

Steps

Iters	Range		Point
8	1.7737391721442364e+105	9.504739634828531e+107	7.111957851088667e+107
10	-2.0025213725199023e+200	-6.204215380457698e+186	-6.299569873792322e+186

simplify7.0ms

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	24	41
1	31	33
2	33	31
done	33	31

end0.0ms

sample2.0s

Algorithm

intervals

Results

791.0ms

8419×

body

valid