Details

sample22.0ms

Algorithm

intervals

Results

13.0ms

300×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	31	21
2	87	21
3	359	21
4	1461	21
done	5000	21

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
3.6b	(- (* b b) (* a a))
9.1b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite173.0ms

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:

22.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
100.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
44.0ms	(/ 1.0 (- (* b b) (* a a)))
31.0ms	(- (* b b) (* a a))
92.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.1s

Counts

513 → 513

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	886	27857
1	2440	25797
done	5001	25719

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 1.0) (+ b a))
0.2b	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
0.3b	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
9.1b	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

572×	`times-frac`
473×	`*-un-lft-identity`
470×	`add-sqr-sqrt`
427×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
112×	`add-exp-log` `add-cbrt-cube`
78×	`associate-r`
58×	`div-inv`
51×	`prod-exp` `cbrt-unprod`
47×	`frac-times`
44×	`sqrt-prod`
33×	`associate-*l/`
31×	`cbrt-undiv` `div-exp`
20×	`pow1`
19×	`associate-*r/`
15×	`associate-l`
13×	`distribute-lft-out`
11×	`distribute-lft-out--`
10×	`pow-prod-down` `difference-of-squares`
9×	`flip3--` `flip--`
8×	`frac-sub`
6×	`associate-/r/` `associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`sub-neg` `flip3-+` `flip-+`
1×	`frac-2neg` `clear-num`

Counts

4 → 618

Calls

4 calls:

6.0ms	(/ (sqrt 1.0) (+ b a))
46.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
218.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
216.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series747.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (sqrt 1.0) (+ b a))
207.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
165.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
297.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.4s

Counts

630 → 630

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	1017	33726
1	2956	31289
done	5000	30917

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-exp-log` `add-cbrt-cube`
47×	`cbrt-undiv` `div-exp`
32×	`times-frac` `prod-exp` `cbrt-unprod`
29×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`associate-/l*`
11×	`associate-l`
10×	`associate-/r*` `associate-/r/`
7×	`associate-/l/`
6×	`pow1` `flip3--` `flip--` `div-inv`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-r` `associate-*l/` `clear-num` `flip-+` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `prod-diff`
1×	`pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

30.0ms	(/ (/ (* (/ (* (/ PI 2.0) 1.0) (- b a)) (- (* 1.0 b) (* a 1.0))) (+ b a)) (* a b))
8.0ms	(/ (* (/ PI 2.0) 1.0) (- b a))
26.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (- b a)) (- (* 1.0 b) (* a 1.0))) (+ b a))
31.0ms	(* (/ (* (/ PI 2.0) 1.0) (- b a)) (- (* 1.0 b) (* a 1.0)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (/ (* (/ (* (/ PI 2.0) 1.0) (- b a)) (- (* 1.0 b) (* a 1.0))) (+ b a)) (* a b))
56.0ms	(/ (* (/ PI 2.0) 1.0) (- b a))
99.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (- b a)) (- (* 1.0 b) (* a 1.0))) (+ b a))
77.0ms	(* (/ (* (/ PI 2.0) 1.0) (- b a)) (- (* 1.0 b) (* a 1.0)))

simplify1.4s

Counts

185 → 185

Iterations

Useful iterations: 2 (647.0ms)

Iter	Nodes	Cost
0	287	4851
1	878	4694
2	4373	3300
done	5000	3300

prune397.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (/ (* 0.5 PI) (+ b a)) (* a b))
0.3b	(/ (* 0.5 PI) (+ b a))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-cbrt-cube`
22×	`times-frac`
16×	`*-un-lft-identity`
12×	`cbrt-undiv` `div-exp`
11×	`associate-/l*`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`prod-exp` `associate-/r/` `cbrt-unprod`
5×	`associate-/r*`
4×	`div-inv` `distribute-lft-out`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 73

Calls

2 calls:

12.0ms	(/ (/ (* 0.5 PI) (+ b a)) (* a b))
7.0ms	(/ (* 0.5 PI) (+ b a))

series125.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (/ (* 0.5 PI) (+ b a)) (* a b))
51.0ms	(/ (* 0.5 PI) (+ b a))

simplify635.0ms

Counts

79 → 79

Iterations

Useful iterations: 2 (177.0ms)

Iter	Nodes	Cost
0	130	1057
1	357	1009
2	1456	823
done	5000	823

prune137.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes51.0ms

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	9	11
1	12	11
done	12	11

end0.0ms

sample563.0ms

Algorithm

intervals

Results

409.0ms

9545×

body

valid