Details

sample41.0ms

Algorithm

intervals

Results

23.0ms

304×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1772
3	378
2	89
1	30
0	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
5.2b	(- (* b b) (* a a))
8.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-cbrt-cube` `add-exp-log`
31×	`add-cube-cbrt`
30×	`associate-r`
14×	`frac-times` `associate-l`
13×	`prod-exp` `cbrt-unprod`
12×	`difference-of-squares`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
8×	`associate-l/` `associate-r/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`associate-/r*` `pow-prod-down` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`clear-num` `frac-2neg` `diff-log`

Counts

4 → 153

Calls

4 calls:

34.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
12.0ms	(/ 1.0 (- (* b b) (* a a)))
14.0ms	(- (* b b) (* a a))
126.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
73.0ms	(/ 1.0 (- (* b b) (* a a)))
43.0ms	(- (* b b) (* a a))
161.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.2s

Counts

165 → 165

Iterations

Iter	Nodes
done	5001
1	873
0	258

prune936.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.7b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
305×	`*-un-lft-identity`
256×	`add-sqr-sqrt`
149×	`add-cube-cbrt`
108×	`associate-r`
61×	`add-cbrt-cube` `add-exp-log`
42×	`distribute-lft-out--`
41×	`difference-of-squares`
37×	`distribute-lft-out`
28×	`associate-/r/`
22×	`cbrt-undiv` `div-exp`
21×	`associate-/l*`
19×	`prod-exp` `cbrt-unprod`
17×	`div-inv`
14×	`frac-times` `associate-l`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-l/` `associate-r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`associate-/l/`

Counts

4 → 358

Calls

4 calls:

17.0ms	(/ 1.0 (+ b a))
29.0ms	(/ (/ 1.0 (+ b a)) (- b a))
111.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
175.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1.0 (+ b a))
78.0ms	(/ (/ 1.0 (+ b a)) (- b a))
124.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
133.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.6s

Counts

370 → 370

Iterations

Iter	Nodes
done	5000
1	1574
0	450

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.3b	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.3b	(* (/ PI 2.0) (/ 1.0 (+ b a)))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
59×	`*-un-lft-identity`
52×	`times-frac`
33×	`add-cube-cbrt`
30×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
15×	`associate-l/` `associate-r/` `associate-/l/`
14×	`associate-l`
11×	`pow1`
9×	`associate-/r*` `flip3--` `flip--`
8×	`frac-sub`
7×	`distribute-lft-out` `distribute-lft-out--`
6×	`associate-/r/` `div-inv` `difference-of-squares`
4×	`pow-prod-down` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`

Counts

4 → 190

Calls

4 calls:

11.0ms	(/ 1.0 (+ b a))
83.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
142.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
57.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1.0 (+ b a))
148.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
164.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
71.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify1.3s

Counts

202 → 202

Iterations

Iter	Nodes
done	5000
1	1008
0	300

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.2b	(/ (* (/ PI 2.0) 1.0) (+ b a))
0.3b	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-cbrt-cube` `add-exp-log`
30×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`times-frac`
17×	`cbrt-undiv` `div-exp`
14×	`prod-exp` `cbrt-unprod`
12×	`associate-r` `add-cube-cbrt`
10×	`associate-l`
9×	`associate-/r*`
8×	`associate-/l/`
7×	`distribute-lft-out--`
6×	`frac-times` `associate-*r/` `associate-/r/` `difference-of-squares`
5×	`pow1` `flip3--` `div-inv` `flip--`
4×	`frac-sub`
3×	`associate-*l/` `distribute-lft-out` `add-log-exp`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `flip-+` `associate-/l*`
1×	`pow-prod-down` `*-commutative` `unswap-sqr`

Counts

3 → 119

Calls

3 calls:

72.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
28.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))
127.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series362.0ms

Counts

3 → 9

Calls

3 calls:

150.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
66.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))
138.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.1s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
1	744
0	227

prune764.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes148.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.5s

9622×

body

valid