Details

sample60.0ms

Algorithm

intervals

Results

37.0ms

300×

body

valid

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	61	21
2	604	21
done	5000	21

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
5.5b	(- (* b b) (* a a))
9.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite376.0ms

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:

78.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
23.0ms	(/ 1.0 (- (* b b) (* a a)))
10.0ms	(- (* b b) (* a a))
215.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
53.0ms	(/ 1.0 (- (* b b) (* a a)))
37.0ms	(- (* b b) (* a a))
123.0ms	(* (* (/ 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
done	5001	24186

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.1b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
9.2b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite518.0ms

Algorithm

rewrite-expression-head

Rules

702×	`times-frac`
557×	`*-un-lft-identity`
528×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
67×	`div-inv`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
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` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 634

Calls

4 calls:

13.0ms	(/ 1.0 (- b a))
135.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
25.0ms	(/ (/ PI 2.0) (+ b a))
292.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ 1.0 (- b a))
90.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
66.0ms	(/ (/ PI 2.0) (+ b a))
136.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.3s

Counts

646 → 646

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	1031	29916
done	5000	26146

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-exp-log` `add-cbrt-cube`
98×	`times-frac`
85×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
46×	`prod-exp` `cbrt-unprod`
30×	`cbrt-undiv` `div-exp`
14×	`pow1` `distribute-lft-out` `associate-/l*`
12×	`associate-*l/`
7×	`div-inv`
6×	`flip3--` `associate-l` `pow-prod-down` `flip--` `associate-/l/`
5×	`associate-/r*`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `associate-r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `frac-2neg` `prod-diff` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 199

Calls

4 calls:

41.0ms	(* (- b a) (* a b))
28.0ms	(/ (/ PI 2.0) (+ b a))
145.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))
121.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* (- b a) (* a b)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (- b a) (* a b))
87.0ms	(/ (/ PI 2.0) (+ b a))
176.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))
207.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* (- b a) (* a b)))

simplify542.0ms

Counts

211 → 211

Iterations

Useful iterations: done (535.0ms)

Iter	Nodes	Cost
0	345	4740
done	5000	4534

prune968.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
103×	`add-exp-log` `add-cbrt-cube`
96×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
42×	`cbrt-undiv` `div-exp`
34×	`prod-exp` `cbrt-unprod`
25×	`associate-/l*`
14×	`distribute-lft-out`
10×	`associate-/r*` `div-inv`
9×	`pow1`
8×	`associate-*l/` `associate-/r/`
7×	`flip3--` `flip--` `associate-/l/`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-r` `pow-prod-down` `clear-num`
2×	`sub-neg` `prod-diff`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

4 → 223

Calls

4 calls:

163.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (- b a)) (* a b))
36.0ms	(/ (/ PI 2.0) (+ b a))
126.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (- b a))
131.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (- b a)) (* a b))
69.0ms	(/ (/ PI 2.0) (+ b a))
167.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (- b a))
150.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))

simplify511.0ms

Counts

235 → 235

Iterations

Useful iterations: done (492.0ms)

Iter	Nodes	Cost
0	382	5677
done	5000	5453

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes73.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	25
1	23	25
done	23	25

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.8s

9623×

body

valid