Details

sample60.0ms

Algorithm

intervals

Results

34.0ms

313×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1772
3	378
2	89
1	30
0	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
3.5b	(- (* b b) (* a a))
7.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-cbrt-cube` `add-exp-log`
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-l/` `associate-r/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`associate-/r*` `pow-prod-down` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`clear-num` `frac-2neg` `diff-log`

Counts

4 → 153

Calls

4 calls:

51.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms	(/ 1.0 (- (* b b) (* a a)))
12.0ms	(- (* b b) (* a a))
136.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
53.0ms	(/ 1.0 (- (* b b) (* a a)))
49.0ms	(- (* b b) (* a a))
142.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.1s

Counts

165 → 165

Iterations

Iter	Nodes
done	5001
1	873
0	258

prune955.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ a b))
7.5b	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-cbrt-cube` `add-exp-log`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-l/` `associate-r/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

9.0ms	(/ 1.0 (- b a))
89.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
17.0ms	(/ (/ PI 2.0) (+ a b))
162.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ 1.0 (- b a))
95.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
72.0ms	(/ (/ PI 2.0) (+ a b))
129.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.5s

Counts

300 → 300

Iterations

Iter	Nodes
done	5000
1	1344
0	407

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
108×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
43×	`add-cbrt-cube` `add-exp-log`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
12×	`associate-r` `distribute-lft-out--`
11×	`div-inv`
10×	`associate-*l/` `difference-of-squares`
9×	`pow1` `associate-/r*`
8×	`associate-/l/`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`associate-/r/`
3×	`sub-neg` `pow-prod-down`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 190

Calls

4 calls:

38.0ms	(- (/ 1.0 a) (/ 1.0 b))
100.0ms	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
26.0ms	(/ (/ PI 2.0) (+ a b))
161.0ms	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (/ 1.0 a) (/ 1.0 b))
131.0ms	(/ (* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
80.0ms	(/ (/ PI 2.0) (+ a b))
184.0ms	(* (* (/ (/ PI 2.0) (+ a b)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.0s

Counts

202 → 202

Iterations

Iter	Nodes
done	5000
1	969
0	337

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

268×	`add-sqr-sqrt`
249×	`times-frac`
221×	`*-un-lft-identity`
85×	`distribute-lft-out--`
73×	`difference-of-squares`
69×	`add-cube-cbrt`
66×	`associate-r`
47×	`add-cbrt-cube` `add-exp-log`
28×	`div-inv`
17×	`cbrt-undiv` `div-exp`
14×	`prod-exp` `cbrt-unprod`
13×	`associate-/l*`
10×	`associate-l`
9×	`associate-/r*`
8×	`associate-/r/`
6×	`pow1` `add-log-exp`
4×	`flip3--` `flip--` `associate-/l/`
3×	`distribute-lft-out`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-*l/` `frac-sub` `flip-+` `unswap-sqr`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 251

Calls

4 calls:

38.0ms	(- (/ 1.0 a) (/ 1.0 b))
162.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ a b)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
90.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
16.0ms	(/ (* (/ PI 2.0) 1.0) (+ a b))

series357.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (/ 1.0 a) (/ 1.0 b))
169.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ a b)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
61.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
79.0ms	(/ (* (/ PI 2.0) 1.0) (+ a b))

simplify1.3s

Counts

263 → 263

Iterations

Iter	Nodes
done	5001
1	1174
0	351

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes147.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

9545×

body

valid