Details

sample43.0ms

Algorithm

intervals

Results

16.0ms

266×

body

valid

simplify5.9s

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	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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.0b	(* z (- t a))
0.5b	(fma x y (* z (- t a)))
21.7b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite42.0ms

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

Counts

4 → 95

Calls

4 calls:

1.0ms	(fma z (- b y) y)
28.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
6.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series784.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma z (- b y) y)
52.0ms	(* z (- t a))
107.0ms	(fma x y (* z (- t a)))
567.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify2.5s

Counts

107 → 107

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	171	1678
1	309	1491
2	699	1283
3	2817	1241
done	5000	1187

prune561.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.5b	(fma x y (* z (- t a)))
0.8b	(/ 1 (fma z (- b y) y))
21.0b	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

rewrite94.0ms

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

Counts

4 → 127

Calls

4 calls:

46.0ms	(* z (- t a))
1.0ms	(fma x y (* z (- t a)))
11.0ms	(/ 1 (fma z (- b y) y))
31.0ms	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

series774.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* z (- t a))
85.0ms	(fma x y (* z (- t a)))
75.0ms	(/ 1 (fma z (- b y) y))
571.0ms	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

simplify3.2s

Counts

139 → 139

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	200	2133
1	387	1818
2	915	1550
3	3816	1508
done	5000	1508

prune608.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x y (+ (* z t) (* z (- a))))
0.8b	(/ 1 (fma z (- b y) y))
1.4b	(+ (* z t) (* z (- a)))
21.0b	(* (fma x y (+ (* z t) (* z (- a)))) (/ 1 (fma z (- b y) y)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

1.0ms	(fma x y (+ (* z t) (* z (- a))))
11.0ms	(/ 1 (fma z (- b y) y))
17.0ms	(+ (* z t) (* z (- a)))
31.0ms	(* (fma x y (+ (* z t) (* z (- a)))) (/ 1 (fma z (- b y) y)))

series806.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma x y (+ (* z t) (* z (- a))))
100.0ms	(/ 1 (fma z (- b y) y))
54.0ms	(+ (* z t) (* z (- a)))
569.0ms	(* (fma x y (+ (* z t) (* z (- a)))) (/ 1 (fma z (- b y) y)))

simplify2.8s

Counts

110 → 110

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	133	1792
1	315	1416
2	957	1245
3	3938	1241
done	5000	1241

prune498.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.4b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.5b	(fma x y (* z (- t a)))
21.7b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite83.0ms

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:

40.0ms	(* z (- t a))
14.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.0ms	(fma x y (* z (- t a)))
9.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series1.2s

Counts

4 → 12

Calls

4 calls:

61.0ms	(* z (- t a))
862.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
87.0ms	(fma x y (* z (- t a)))
176.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify2.8s

Counts

175 → 175

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	264	3896
1	509	3507
2	1078	3118
3	4059	3058
done	5000	3058

prune571.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 9.8b

regimes707.0ms

Accuracy

34.4% (8.2b remaining)

Error of 19.1b against oracle of 10.9b and baseline of 23.3b

bsearch169.0ms

Steps

Iters	Range		Point
10	1.5005533500003862e+154	1.421934971328253e+171	5.1156121506382365e+154
9	-6.706721591036622e+138	-1.26417539014382e+131	-1.3832283572379638e+135

simplify9.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	25	42
1	36	36
2	40	36
3	41	36
done	41	36

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.5s

8419×

body

valid