Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

298×

body

valid

simplify39.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	90	10
2	384	10
3	1828	10
4	5001	10
done	5001	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
4.1b	(- (* b b) (* a a))
11.1b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

515×	`times-frac`
419×	`add-sqr-sqrt`
403×	`*-un-lft-identity`
395×	`add-cube-cbrt`
339×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
57×	`div-inv`
36×	`add-exp-log` `add-cbrt-cube`
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×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `fma-neg` `diff-log` `clear-num`

Counts

4 → 501

Calls

4 calls:

41.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
12.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
139.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
43.0ms	(/ 1.0 (- (* b b) (* a a)))
32.0ms	(- (* b b) (* a a))
93.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify144.0ms

Counts

513 → 513

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008
done	5002	13008

prune908.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
11.1b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite345.0ms

Algorithm

rewrite-expression-head

Rules

820×	`times-frac`
669×	`*-un-lft-identity`
620×	`add-sqr-sqrt`
513×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
108×	`associate-r`
69×	`div-inv`
61×	`add-exp-log` `add-cbrt-cube`
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`
14×	`frac-times` `associate-l`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `frac-sub` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 704

Calls

4 calls:

11.0ms	(/ 1.0 (+ b a))
27.0ms	(/ (/ 1.0 (+ b a)) (- b a))
80.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
169.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (+ b a))
54.0ms	(/ (/ 1.0 (+ b a)) (- b a))
63.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
99.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify177.0ms

Counts

716 → 716

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	3140	16922
1	5003	15938
done	5003	15938

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
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)))

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

520×	`times-frac`
425×	`add-sqr-sqrt`
423×	`*-un-lft-identity`
397×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
61×	`add-exp-log` `add-cbrt-cube`
58×	`div-inv`
30×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
11×	`pow1`
9×	`flip3--` `associate-/r*` `flip--`
8×	`frac-sub`
7×	`distribute-lft-out` `distribute-lft-out--`
6×	`associate-/r/` `difference-of-squares`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`sub-neg` `frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`

Counts

4 → 536

Calls

4 calls:

10.0ms	(/ 1.0 (+ b a))
146.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
129.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
38.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 1.0 (+ b a))
100.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
108.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
54.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify147.0ms

Counts

548 → 548

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2634	13861
1	5001	12813
done	5001	12813

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 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) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
0.2b	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.4b	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite398.0ms

Algorithm

rewrite-expression-head

Rules

809×	`times-frac`
641×	`*-un-lft-identity`
633×	`add-sqr-sqrt`
587×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
91×	`div-inv`
47×	`add-exp-log` `add-cbrt-cube`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
16×	`cbrt-undiv` `div-exp` `associate-/r/`
15×	`prod-exp` `cbrt-unprod`
13×	`fma-neg`
12×	`associate-r`
11×	`associate-/l*`
10×	`associate-*l/`
9×	`pow1` `associate-/r*`
8×	`associate-/l/` `distribute-lft-out`
7×	`flip3-+` `flip-+`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`diff-log` `associate-l` `*-commutative`

Counts

4 → 714

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
68.0ms	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
126.0ms	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
111.0ms	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
99.0ms	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
111.0ms	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
64.0ms	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify168.0ms

Counts

726 → 726

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2578	17411
1	5001	15285
done	5001	15285

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes60.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	8
1	14	8
done	14	8

end0.0ms

sample611.0ms

Algorithm

intervals

Results

406.0ms

9590×

body

valid