Details

sample44.0ms

Algorithm

intervals

Results

22.0ms

306×

body

valid

simplify4.1s

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.1b	(/ 1.0 (- (* b b) (* a a)))
4.4b	(- (* b b) (* a a))
8.3b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite649.0ms

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` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log`

Counts

4 → 505

Calls

4 calls:

101.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
36.0ms	(/ 1.0 (- (* b b) (* a a)))
22.0ms	(- (* b b) (* a a))
331.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
105.0ms	(/ 1.0 (- (* b b) (* a a)))
79.0ms	(- (* b b) (* a a))
174.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify6.1s

Counts

517 → 517

Iterations

Iter	Nodes
done	5002
1	2890
0	890

prune8.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 1.0) (+ b a))
0.1b	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
0.4b	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
8.3b	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

572×	`times-frac`
473×	`*-un-lft-identity`
470×	`add-sqr-sqrt`
427×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
112×	`add-cbrt-cube` `add-exp-log`
78×	`associate-r`
58×	`div-inv`
51×	`prod-exp` `cbrt-unprod`
47×	`frac-times`
44×	`sqrt-prod`
33×	`associate-*l/`
31×	`cbrt-undiv` `div-exp`
20×	`pow1`
19×	`associate-*r/`
15×	`associate-l`
13×	`distribute-lft-out`
11×	`distribute-lft-out--`
10×	`pow-prod-down` `difference-of-squares`
9×	`flip3--` `flip--`
8×	`frac-sub`
6×	`associate-/r/` `associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`sub-neg` `flip3-+` `flip-+`
1×	`clear-num` `frac-2neg`

Counts

4 → 622

Calls

4 calls:

17.0ms	(/ (sqrt 1.0) (+ b a))
178.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
73.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
720.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series1.3s

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (sqrt 1.0) (+ b a))
380.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
262.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
504.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify6.9s

Counts

634 → 634

Iterations

Iter	Nodes
done	5003
1	3440
0	1021

prune8.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* (* (/ PI 2.0) (sqrt 1.0)) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.3b	(* (* (* (/ PI 2.0) (sqrt 1.0)) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (* (/ PI 2.0) (sqrt 1.0)) (/ (sqrt 1.0) (- b a)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

765×	`times-frac`
617×	`add-sqr-sqrt`
613×	`*-un-lft-identity`
581×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
92×	`add-cbrt-cube` `add-exp-log`
85×	`div-inv`
48×	`associate-r`
44×	`prod-exp` `cbrt-unprod`
33×	`associate-*l/`
27×	`frac-times`
23×	`cbrt-undiv` `div-exp`
18×	`pow1`
16×	`distribute-lft-out--`
15×	`associate-*r/` `sqrt-prod` `associate-/l/`
14×	`difference-of-squares`
13×	`fma-neg`
10×	`flip3--` `flip--`
9×	`pow-prod-down` `frac-sub`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg`
2×	`associate-l` `*-commutative` `distribute-lft-out`
1×	`clear-num` `frac-2neg` `flip3-+` `diff-log` `flip-+` `associate-/l*`

Counts

4 → 725

Calls

4 calls:

82.0ms	(- (/ 1.0 a) (/ 1.0 b))
516.0ms	(/ (* (* (* (/ PI 2.0) (sqrt 1.0)) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
478.0ms	(* (* (* (/ PI 2.0) (sqrt 1.0)) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
97.0ms	(* (* (/ PI 2.0) (sqrt 1.0)) (/ (sqrt 1.0) (- b a)))

series1.3s

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ 1.0 a) (/ 1.0 b))
545.0ms	(/ (* (* (* (/ PI 2.0) (sqrt 1.0)) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
356.0ms	(* (* (* (/ PI 2.0) (sqrt 1.0)) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
380.0ms	(* (* (/ PI 2.0) (sqrt 1.0)) (/ (sqrt 1.0) (- b a)))

simplify6.6s

Counts

737 → 737

Iterations

Iter	Nodes
done	5000
1	3119
0	945

prune9.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (* (/ (* 1.0 PI) (* a b)) 0.5) (+ b a))
0.5b	(/ (* 1.0 PI) (* a b))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-cbrt-cube` `add-exp-log`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity`
5×	`associate-/r*` `times-frac`
4×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `associate-/r/` `insert-posit16` `log1p-expm1-u` `div-inv` `distribute-lft-out` `associate-/l*` `add-log-exp`
1×	`flip3-+` `associate-*l/` `flip-+` `associate-/l/`

Counts

2 → 61

Calls

2 calls:

50.0ms	(/ (* (/ (* 1.0 PI) (* a b)) 0.5) (+ b a))
35.0ms	(/ (* 1.0 PI) (* a b))

series171.0ms

Counts

2 → 6

Calls

2 calls:

107.0ms	(/ (* (/ (* 1.0 PI) (* a b)) 0.5) (+ b a))
64.0ms	(/ (* 1.0 PI) (* a b))

simplify3.7s

Counts

67 → 67

Iterations

Iter	Nodes
done	5247
2	2006
1	381
0	129

prune693.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes533.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

9533×

body

valid