Details

sample24.0ms

Algorithm

intervals

Results

13.0ms

308×

body

valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	31	21
2	90	21
3	384	21
4	1663	21
done	5000	21

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize13.0ms

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)))
3.7b	(- (* b b) (* a a))
8.4b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite258.0ms

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:

45.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
148.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
43.0ms	(/ 1.0 (- (* b b) (* a a)))
32.0ms	(- (* b b) (* a a))
92.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.2s

Counts

513 → 513

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	886	27857
1	2290	25797
done	5000	22403

prune874.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
0.2b	(/ (/ 1.0 (+ b a)) (- b a))
8.4b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite354.0ms

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:

10.0ms	(/ 1.0 (+ b a))
80.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
29.0ms	(/ (/ 1.0 (+ b a)) (- b a))
175.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (+ b a))
67.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
54.0ms	(/ (/ 1.0 (+ b a)) (- b a))
103.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.6s

Counts

716 → 716

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	1075	31669
1	2912	29273
done	5000	25741

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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

rewrite374.0ms

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))
149.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
36.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))
134.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (+ b a))
98.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
58.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))
110.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.3s

Counts

548 → 548

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	925	25612
1	2437	23502
done	5001	19972

prune988.0ms

Pruning

8 alts after pruning (8 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)))
0.2b	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
0.3b	(/ (* (/ PI 2.0) 1.0) (+ b a))

rewrite327.0ms

Algorithm

rewrite-expression-head

Rules

492×	`times-frac`
457×	`add-sqr-sqrt`
410×	`*-un-lft-identity`
258×	`add-cube-cbrt`
169×	`prod-diff`
85×	`distribute-lft-out--`
73×	`difference-of-squares`
66×	`associate-r`
55×	`div-inv`
47×	`add-exp-log` `add-cbrt-cube`
17×	`cbrt-undiv` `div-exp`
14×	`prod-exp` `cbrt-unprod`
13×	`fma-neg` `associate-/l*`
10×	`associate-l`
9×	`associate-/r*`
8×	`associate-/r/`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
3×	`distribute-lft-out`
2×	`frac-2neg` `flip3-+` `associate-*l/` `clear-num` `frac-sub` `flip-+` `unswap-sqr`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 441

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
147.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
90.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
20.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))

series247.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
104.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
56.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
55.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))

simplify722.0ms

Counts

453 → 453

Iterations

Useful iterations: done (701.0ms)

Iter	Nodes	Cost
0	605	13128
1	1599	11850
done	5001	9536

prune935.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes61.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample625.0ms

Algorithm

intervals

Results

426.0ms

9596×

body

valid