Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

304×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	30	21
2	86	21
3	352	21
4	1416	21
done	5000	21

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b	(/ 1.0 (- (* b b) (* a a)))
3.8b	(- (* b b) (* a a))
9.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
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-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 153

Calls

4 calls:

21.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
68.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
40.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
90.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.3s

Counts

165 → 165

Iterations

Useful iterations: 2 (617.0ms)

Iter	Nodes	Cost
0	258	3239
1	802	3164
2	3518	2682
done	5001	2682

prune438.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
9.8b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

350×	`times-frac`
298×	`*-un-lft-identity`
261×	`add-sqr-sqrt`
142×	`add-cube-cbrt`
108×	`associate-r`
59×	`add-exp-log` `add-cbrt-cube`
47×	`distribute-lft-out--`
45×	`difference-of-squares`
33×	`distribute-lft-out`
26×	`associate-/r/`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
18×	`div-inv` `associate-/l*`
14×	`frac-times` `associate-l`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 347

Calls

4 calls:

16.0ms	(- (/ 1.0 a) (/ 1.0 b))
15.0ms	(/ (/ 1.0 (+ b a)) (- b a))
60.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
97.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
51.0ms	(/ (/ 1.0 (+ b a)) (- b a))
59.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
95.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify524.0ms

Counts

359 → 359

Iterations

Useful iterations: done (508.0ms)

Iter	Nodes	Cost
0	463	7064
1	1502	6659
done	5000	6639

prune845.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (* (/ 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)))
0.4b	(* (/ PI 2.0) (/ 1.0 (+ b a)))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 179

Calls

4 calls:

16.0ms	(- (/ 1.0 a) (/ 1.0 b))
50.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
260.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
21.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
91.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
99.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
54.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify1.8s

Counts

191 → 191

Iterations

Useful iterations: 2 (945.0ms)

Iter	Nodes	Cost
0	304	3703
1	987	3582
2	4548	2962
done	5000	2962

prune455.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (/ (* (/ 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))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
36.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
77.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))
8.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))

series287.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
101.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
101.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))
53.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))

simplify1.3s

Counts

153 → 153

Iterations

Useful iterations: 2 (683.0ms)

Iter	Nodes	Cost
0	247	3005
1	752	2921
2	3491	2399
done	5000	2399

prune322.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes80.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	18	21
done	18	21

end0.0ms

sample560.0ms

Algorithm

intervals

Results

412.0ms

9589×

body

valid