Details

sample36.0ms

Algorithm

intervals

Results

20.0ms

311×

body

valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1569
3	370
2	89
1	31
0	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize37.0ms

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)))
4.6b	(- (* b b) (* a a))
7.4b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite326.0ms

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-cbrt-cube` `add-exp-log`
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×	`distribute-lft-out--`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log`

Counts

4 → 501

Calls

4 calls:

46.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
20.0ms	(/ 1.0 (- (* b b) (* a a)))
13.0ms	(- (* b b) (* a a))
179.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
81.0ms	(/ 1.0 (- (* b b) (* a a)))
61.0ms	(- (* b b) (* a a))
139.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify3.0s

Counts

513 → 513

Iterations

Iter	Nodes
done	5000
1	2893
0	886

prune4.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.2b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
7.4b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite509.0ms

Algorithm

rewrite-expression-head

Rules

820×	`times-frac`
669×	`*-un-lft-identity`
620×	`add-sqr-sqrt`
513×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
108×	`associate-r`
69×	`div-inv`
61×	`add-cbrt-cube` `add-exp-log`
42×	`distribute-lft-out--`
41×	`difference-of-squares`
37×	`distribute-lft-out`
28×	`associate-/r/`
22×	`cbrt-undiv` `div-exp`
21×	`associate-/l*`
19×	`prod-exp` `cbrt-unprod`
14×	`frac-times` `associate-l`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`associate-/r*`
8×	`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×	`clear-num` `sub-neg` `frac-2neg` `*-commutative`
1×	`associate-/l/`

Counts

4 → 704

Calls

4 calls:

17.0ms	(/ 1.0 (+ b a))
45.0ms	(/ (/ 1.0 (+ b a)) (- b a))
103.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
238.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1.0 (+ b a))
65.0ms	(/ (/ 1.0 (+ b a)) (- b a))
97.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
147.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify3.5s

Counts

716 → 716

Iterations

Iter	Nodes
done	5000
1	3562
0	1075

prune5.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.2b	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.4b	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (/ PI 2.0) (/ 1.0 (+ b a)))

rewrite540.0ms

Algorithm

rewrite-expression-head

Rules

520×	`times-frac`
425×	`add-sqr-sqrt`
423×	`*-un-lft-identity`
397×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
61×	`add-cbrt-cube` `add-exp-log`
58×	`div-inv`
30×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
15×	`associate-l/` `associate-r/` `associate-/l/`
14×	`associate-l`
11×	`pow1`
9×	`associate-/r*` `flip3--` `flip--`
8×	`frac-sub`
7×	`distribute-lft-out` `distribute-lft-out--`
6×	`associate-/r/` `difference-of-squares`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`clear-num` `sub-neg` `frac-2neg` `flip3-+` `*-commutative` `flip-+`

Counts

4 → 536

Calls

4 calls:

9.0ms	(/ 1.0 (+ b a))
194.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
228.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
45.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ 1.0 (+ b a))
165.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
172.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
85.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify3.5s

Counts

548 → 548

Iterations

Iter	Nodes
done	5000
1	3039
0	925

prune4.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize46.0ms

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))

rewrite408.0ms

Algorithm

rewrite-expression-head

Rules

492×	`times-frac`
457×	`add-sqr-sqrt`
410×	`*-un-lft-identity`
258×	`add-cube-cbrt`
169×	`prod-diff`
85×	`distribute-lft-out--`
73×	`difference-of-squares`
66×	`associate-r`
55×	`div-inv`
47×	`add-cbrt-cube` `add-exp-log`
17×	`cbrt-undiv` `div-exp`
14×	`prod-exp` `cbrt-unprod`
13×	`fma-neg` `associate-/l*`
10×	`associate-l`
9×	`associate-/r*`
8×	`associate-/r/`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `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 → 441

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
197.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ a b)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
107.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
16.0ms	(/ (* (/ PI 2.0) 1.0) (+ a b))

series356.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (/ 1.0 a) (/ 1.0 b))
138.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ a b)) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
62.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
109.0ms	(/ (* (/ PI 2.0) 1.0) (+ a b))

simplify1.9s

Counts

453 → 453

Iterations

Iter	Nodes
done	5001
1	1712
0	606

prune2.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes566.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.2s

9598×

body

valid