Details

sample41.0ms

Algorithm

intervals

Results

26.0ms

310×

body

valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	30	21
2	89	21
3	377	21
4	1644	21
done	5000	21

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize21.0ms

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)))
5.1b	(- (* b b) (* a a))
7.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite300.0ms

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:

71.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
15.0ms	(/ 1.0 (- (* b b) (* a a)))
12.0ms	(- (* b b) (* a a))
190.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
64.0ms	(/ 1.0 (- (* b b) (* a a)))
39.0ms	(- (* b b) (* a a))
152.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.8s

Counts

165 → 165

Iterations

Useful iterations: 2 (729.0ms)

Iter	Nodes	Cost
0	258	3239
1	776	3164
2	3267	2690
done	5000	2690

prune506.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite490.0ms

Algorithm

rewrite-expression-head

Rules

286×	`add-sqr-sqrt`
265×	`times-frac`
232×	`*-un-lft-identity`
85×	`distribute-lft-out--`
80×	`add-cube-cbrt`
79×	`associate-l`
73×	`difference-of-squares`
59×	`add-exp-log` `add-cbrt-cube`
28×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
19×	`associate-r`
18×	`cbrt-undiv` `div-exp`
12×	`associate-/l*`
11×	`pow1`
6×	`frac-times` `associate-*r/` `associate-/r/` `add-log-exp`
5×	`associate-/r*`
4×	`flip3--` `pow-prod-down` `associate-*l/` `flip--` `unswap-sqr`
3×	`associate-/l/` `distribute-lft-out`
2×	`*-commutative` `frac-sub`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `clear-num` `flip-+`

Counts

4 → 276

Calls

4 calls:

26.0ms	(- (/ 1.0 a) (/ 1.0 b))
156.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
185.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
98.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series366.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (/ 1.0 a) (/ 1.0 b))
138.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
106.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
83.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

simplify2.3s

Counts

288 → 288

Iterations

Useful iterations: 2 (964.0ms)

Iter	Nodes	Cost
0	388	6213
1	1181	6052
2	3636	5342
done	5001	5342

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite540.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-sqr-sqrt`
143×	`times-frac`
132×	`*-un-lft-identity`
56×	`add-exp-log` `add-cbrt-cube`
48×	`distribute-lft-out--`
46×	`add-cube-cbrt`
41×	`difference-of-squares`
20×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
17×	`div-inv`
13×	`associate-l` `associate-/l*`
9×	`pow1` `associate-/r*`
6×	`associate-*l/` `associate-/l/` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`frac-times` `frac-2neg` `associate-*r/` `clear-num` `frac-sub` `distribute-lft-out`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-r` `*-commutative` `flip-+`

Counts

4 → 194

Calls

4 calls:

52.0ms	(- (/ 1.0 a) (/ 1.0 b))
176.0ms	(/ (* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (+ b a))
117.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
171.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

series355.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
129.0ms	(/ (* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (+ b a))
77.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
112.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

simplify1.6s

Counts

206 → 206

Iterations

Useful iterations: 2 (688.0ms)

Iter	Nodes	Cost
0	325	4481
1	879	4338
2	2844	3698
done	5000	3698

prune762.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

163×	`add-sqr-sqrt`
148×	`times-frac`
136×	`*-un-lft-identity`
48×	`add-cube-cbrt` `distribute-lft-out--`
47×	`add-exp-log` `add-cbrt-cube`
41×	`difference-of-squares`
18×	`div-inv`
17×	`cbrt-undiv` `div-exp`
14×	`prod-exp` `cbrt-unprod`
13×	`associate-l` `associate-/l*`
10×	`associate-r`
9×	`associate-/r*`
6×	`pow1` `associate-/r/` `add-log-exp`
4×	`associate-/l/`
3×	`flip3--` `flip--` `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 → 198

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
154.0ms	(* (/ PI 2.0) (/ (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0) (+ b a)))
64.0ms	(/ (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0) (+ b a))
100.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series384.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (/ 1.0 a) (/ 1.0 b))
144.0ms	(* (/ PI 2.0) (/ (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0) (+ b a)))
124.0ms	(/ (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0) (+ b a))
73.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

simplify1.7s

Counts

210 → 210

Iterations

Useful iterations: 2 (686.0ms)

Iter	Nodes	Cost
0	324	4600
1	886	4458
2	2883	3878
done	5000	3878

prune838.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes69.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.7s

9560×

body

valid