Details

sample39.0ms

Algorithm

intervals

Results

23.0ms

304×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1848
3	385
2	90
1	31
0	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
5.2b	(- (* b b) (* a a))
8.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite287.0ms

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:

35.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
10.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
169.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
82.0ms	(/ 1.0 (- (* b b) (* a a)))
49.0ms	(- (* b b) (* a a))
108.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.8s

Counts

513 → 513

Iterations

Iter	Nodes
done	5000
1	2914
0	886

prune4.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.7b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite442.0ms

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))
36.0ms	(/ (/ 1.0 (+ b a)) (- b a))
94.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
223.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1.0 (+ b a))
51.0ms	(/ (/ 1.0 (+ b a)) (- b a))
85.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
108.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.7s

Counts

716 → 716

Iterations

Iter	Nodes
done	5002
1	3626
0	1075

prune5.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite451.0ms

Algorithm

rewrite-expression-head

Rules

504×	`times-frac`
411×	`*-un-lft-identity`
406×	`add-sqr-sqrt`
389×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
57×	`div-inv`
52×	`add-cbrt-cube` `add-exp-log`
30×	`associate-r`
21×	`prod-exp` `cbrt-unprod`
17×	`associate-*r/`
13×	`cbrt-undiv` `div-exp`
11×	`pow1`
7×	`distribute-lft-out` `associate-/l/`
6×	`frac-times` `associate-/r/`
5×	`associate-/r*` `flip3--` `flip--` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `frac-sub` `log1p-expm1-u` `associate-/l*` `add-log-exp` `difference-of-squares`
2×	`clear-num` `sub-neg` `frac-2neg` `flip3-+` `associate-l/` `-commutative` `flip-+` `unswap-sqr`

Counts

4 → 494

Calls

4 calls:

18.0ms	(/ 1.0 (+ b a))
209.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
137.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
29.0ms	(* PI (/ 1.0 (+ b a)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ 1.0 (+ b a))
142.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
137.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
63.0ms	(* PI (/ 1.0 (+ b a)))

simplify3.3s

Counts

506 → 506

Iterations

Iter	Nodes
done	5002
1	2821
0	859

prune4.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
0.2b	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.3b	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite438.0ms

Algorithm

rewrite-expression-head

Rules

500×	`times-frac`
392×	`*-un-lft-identity`
388×	`add-sqr-sqrt`
376×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
58×	`div-inv`
49×	`add-cbrt-cube` `add-exp-log`
17×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
12×	`associate-r`
11×	`associate-/l*`
8×	`pow1` `associate-*r/` `associate-/r/`
5×	`associate-/r*` `distribute-lft-out--`
4×	`distribute-lft-out` `difference-of-squares` `associate-/l/`
3×	`expm1-log1p-u` `flip3-+` `flip3--` `pow-prod-down` `flip-+` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`clear-num` `sub-neg` `frac-2neg` `frac-sub`
1×	`associate-l` `*-commutative`

Counts

3 → 458

Calls

3 calls:

93.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
155.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
155.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series347.0ms

Counts

3 → 9

Calls

3 calls:

133.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
124.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
91.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.6s

Counts

467 → 467

Iterations

Iter	Nodes
done	5000
1	2697
0	846

prune3.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes178.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

9622×

body

valid