Details

sample50.0ms

Algorithm

intervals

Results

28.0ms

300×

body

valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.2b	(/ 1.0 (- (* b b) (* a a)))
5.0b	(- (* b b) (* a a))
10.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite289.0ms

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:

70.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
18.0ms	(/ 1.0 (- (* b b) (* a a)))
16.0ms	(- (* b b) (* a a))
172.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
81.0ms	(/ 1.0 (- (* b b) (* a a)))
36.0ms	(- (* b b) (* a a))
141.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.5s

Counts

165 → 165

Iterations

Useful iterations: 2 (717.0ms)

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

prune558.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

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)) (/ 1.0 (+ b a)))
0.2b	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

rewrite543.0ms

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:

52.0ms	(- (/ 1.0 a) (/ 1.0 b))
195.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
167.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
108.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series313.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
121.0ms	(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
102.0ms	(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
57.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

simplify2.4s

Counts

288 → 288

Iterations

Useful iterations: 2 (1.3s)

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

prune854.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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)))

rewrite617.0ms

Algorithm

rewrite-expression-head

Rules

286×	`add-sqr-sqrt`
265×	`times-frac`
232×	`*-un-lft-identity`
85×	`distribute-lft-out--`
84×	`associate-r`
80×	`add-cube-cbrt`
73×	`difference-of-squares`
59×	`add-exp-log` `add-cbrt-cube`
28×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
14×	`associate-l`
12×	`associate-/l*`
11×	`pow1`
6×	`frac-times` `associate-*l/` `associate-/r/` `add-log-exp`
5×	`associate-/r*`
4×	`flip3--` `associate-*r/` `pow-prod-down` `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:

40.0ms	(- (/ 1.0 a) (/ 1.0 b))
260.0ms	(* (* (/ PI 2.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))) (/ 1.0 (+ b a)))
94.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
187.0ms	(* (/ PI 2.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (/ 1.0 a) (/ 1.0 b))
112.0ms	(* (* (/ PI 2.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))) (/ 1.0 (+ b a)))
53.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
95.0ms	(* (/ PI 2.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))

simplify2.1s

Counts

288 → 288

Iterations

Useful iterations: 2 (842.0ms)

Iter	Nodes	Cost
0	393	5956
1	1187	5687
2	4296	5009
done	5001	5009

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.0b	(* 0.5 (/ PI (* a b)))
0.2b	(* (* 0.5 (/ PI (* a b))) (/ 1.0 (+ b a)))
0.7b	(/ PI (* a b))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
40×	`*-un-lft-identity`
30×	`times-frac`
28×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`associate-r`
21×	`prod-exp` `cbrt-unprod`
13×	`cbrt-undiv` `div-exp`
11×	`pow1`
7×	`distribute-lft-out`
6×	`associate-/l*`
5×	`associate-/r*`
4×	`associate-r/` `associate-l*` `pow-prod-down` `associate-/r/` `div-inv` `add-log-exp`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`frac-times` `associate-*l/` `unswap-sqr`

Counts

4 → 129

Calls

4 calls:

11.0ms	(/ 1.0 (+ b a))
42.0ms	(* 0.5 (/ PI (* a b)))
105.0ms	(* (* 0.5 (/ PI (* a b))) (/ 1.0 (+ b a)))
16.0ms	(/ PI (* a b))

series245.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1.0 (+ b a))
65.0ms	(* 0.5 (/ PI (* a b)))
94.0ms	(* (* 0.5 (/ PI (* a b))) (/ 1.0 (+ b a)))
32.0ms	(/ PI (* a b))

simplify1.6s

Counts

141 → 141

Iterations

Useful iterations: 2 (406.0ms)

Iter	Nodes	Cost
0	176	1755
1	465	1663
2	1952	1339
done	5000	1339

prune350.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes88.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	15
1	19	15
done	19	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

765.0ms

9518×

body

valid