Details

sample69.0ms

Algorithm

intervals

Results

56.0ms

314×

body

valid

simplify441.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

440.0ms

(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.2b

localize50.0ms

Local error

Found 4 expressions with local error:

9.3b	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
4.2b	(- (* b b) (* a a))
1.2b	(/ 1 (- (* b b) (* a a)))
0.2b	(* (/ PI 2) (/ 1 (- (* b b) (* a a))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

526×	`times-frac`
436×	`add-sqr-sqrt`
413×	`*-un-lft-identity`
395×	`add-cube-cbrt`
339×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
62×	`add-exp-log`
59×	`div-inv`
37×	`associate-r`
36×	`add-cbrt-cube`
25×	`prod-exp`
18×	`div-exp`
17×	`frac-times` `difference-of-squares`
14×	`associate-l`
13×	`cbrt-unprod`
12×	`pow1`
9×	`cbrt-undiv` `associate-*l/`
8×	`flip3--` `associate-*r/` `flip--`
7×	`distribute-lft-out--`
6×	`add-log-exp` `unswap-sqr`
5×	`rec-exp` `1-exp` `un-div-inv` `frac-sub`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 531

Calls

4 calls:

Slowest

94.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
32.0ms	(* (/ PI 2) (/ 1 (- (* b b) (* a a))))
14.0ms	(/ 1 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))

series289.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

99.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
78.0ms	(* (/ PI 2) (/ 1 (- (* b b) (* a a))))
56.0ms	(/ 1 (- (* b b) (* a a)))
55.0ms	(- (* b b) (* a a))

simplify2.9m

Counts

521 → 543

Calls

521 calls:

Slowest

1.1s	(* (fma (- (/ 1 (cbrt b))) (/ 1 (* (cbrt b) (cbrt b))) (* (/ 1 (cbrt b)) (/ 1 (* (cbrt b) (cbrt b))))) (* (/ PI 2) (/ 1 (- (* b b) (* a a)))))
939.0ms	(* (fma (- (/ (cbrt 1) (sqrt b))) (/ (* (cbrt 1) (cbrt 1)) (sqrt b)) (* (/ (cbrt 1) (sqrt b)) (/ (* (cbrt 1) (cbrt 1)) (sqrt b)))) (* (/ PI 2) (/ 1 (- (* b b) (* a a)))))
840.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (fma (- (sqrt (/ 1 b))) (sqrt (/ 1 b)) (* (sqrt (/ 1 b)) (sqrt (/ 1 b)))))
835.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (fma (- (sqrt (/ 1 b))) (sqrt (/ 1 b)) (* (sqrt (/ 1 b)) (sqrt (/ 1 b)))))
804.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (fma (- (/ 1 b)) (/ 1 1) (* (/ 1 b) (/ 1 1))))

prune7.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ PI (+ b a))
0.2b	(/ (/ PI (+ b a)) (* 2 (* a b)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`add-cbrt-cube` `add-exp-log`
21×	`associate-/l*`
10×	`cbrt-undiv` `div-exp` `distribute-lft-out`
6×	`prod-exp` `associate-/r/` `cbrt-unprod`
5×	`associate-/r*`
4×	`div-inv`
3×	`flip3-+` `flip-+`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 99

Calls

2 calls:

Slowest

46.0ms	(/ (/ PI (+ b a)) (* 2 (* a b)))
16.0ms	(/ PI (+ b a))

series171.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

102.0ms	(/ (/ PI (+ b a)) (* 2 (* a b)))
69.0ms	(/ PI (+ b a))

simplify8.0s

Counts

105 → 105

Calls

105 calls:

Slowest

569.0ms	(/ (/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a))) (* (* (* 2 2) 2) (* (* (* a a) a) (* (* b b) b))))
514.0ms	(/ (/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a))) (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))))
490.0ms	(/ (* (* (/ PI (+ b a)) (/ PI (+ b a))) (/ PI (+ b a))) (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))))
436.0ms	(- (- (log PI) (log (+ b a))) (log (* 2 (* a b))))
410.0ms	(- (log (/ PI (+ b a))) (+ (log 2) (log (* a b))))

prune951.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ 1 (/ (+ b a) PI))
0.3b	(/ (+ b a) PI)
0.2b	(/ (/ 1 (/ (+ b a) PI)) (* 2 (* a b)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

329×	`times-frac`
211×	`*-un-lft-identity`
143×	`add-sqr-sqrt` `add-cube-cbrt`
94×	`add-exp-log`
60×	`associate-/l*`
50×	`div-exp`
46×	`add-cbrt-cube`
34×	`distribute-lft-out`
22×	`cbrt-undiv`
21×	`prod-exp`
20×	`associate-/r*`
15×	`div-inv`
9×	`cbrt-unprod`
8×	`rec-exp` `1-exp`
4×	`pow1`
3×	`expm1-log1p-u` `clear-num` `frac-2neg` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
1×	`flip3-+` `flip-+` `pow-flip` `inv-pow`

Counts

3 → 278

Calls

3 calls:

Slowest

35.0ms	(/ (/ 1 (/ (+ b a) PI)) (* 2 (* a b)))
29.0ms	(/ (+ b a) PI)
27.0ms	(/ 1 (/ (+ b a) PI))

series224.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

89.0ms	(/ (/ 1 (/ (+ b a) PI)) (* 2 (* a b)))
73.0ms	(/ (+ b a) PI)
62.0ms	(/ 1 (/ (+ b a) PI))

simplify40.2s

Counts

350 → 287

Calls

350 calls:

Slowest

1.2s	(/ (* (* (/ 1 (/ (+ b a) PI)) (/ 1 (/ (+ b a) PI))) (/ 1 (/ (+ b a) PI))) (* (* (* 2 2) 2) (* (* (* a b) (* a b)) (* a b))))
1.1s	(/ (* (* (/ 1 (/ (+ b a) PI)) (/ 1 (/ (+ b a) PI))) (/ 1 (/ (+ b a) PI))) (* (* (* 2 2) 2) (* (* (* a a) a) (* (* b b) b))))
960.0ms	(/ (* (* (/ 1 (/ (+ b a) PI)) (/ 1 (/ (+ b a) PI))) (/ 1 (/ (+ b a) PI))) (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))))
593.0ms	(/ (/ (* (* 1 1) 1) (/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* PI PI) PI))) (* (* (* 2 2) 2) (* (* (* a a) a) (* (* b b) b))))
552.0ms	(/ (/ (* (* 1 1) 1) (/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* PI PI) PI))) (* (* (* 2 2) 2) (* (* (* a b) (* a b)) (* a b))))

prune2.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ PI a)
0.2b	(/ (/ PI a) b)
0.2b	(* (/ 1/2 (+ a b)) (/ (/ PI a) b))
0.0b	(/ 1/2 (+ a b))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

183×	`times-frac`
127×	`add-sqr-sqrt`
120×	`*-un-lft-identity`
106×	`add-cube-cbrt`
43×	`associate-r`
34×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/l*`
18×	`associate-l`
14×	`cbrt-undiv` `div-exp`
12×	`div-inv`
10×	`associate-/r*`
7×	`distribute-lft-out`
6×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`flip3-+` `flip-+`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 233

Calls

4 calls:

Slowest

44.0ms	(* (/ 1/2 (+ a b)) (/ (/ PI a) b))
15.0ms	(/ (/ PI a) b)
9.0ms	(/ 1/2 (+ a b))
8.0ms	(/ PI a)

series227.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

89.0ms	(* (/ 1/2 (+ a b)) (/ (/ PI a) b))
79.0ms	(/ 1/2 (+ a b))
31.0ms	(/ PI a)
29.0ms	(/ (/ PI a) b)

simplify12.2s

Counts

252 → 245

Calls

252 calls:

Slowest

784.0ms	(+ (log (/ 1/2 (+ a b))) (- (log (/ PI a)) (log b)))
605.0ms	(* (/ (* (* 1/2 1/2) 1/2) (* (* (+ a b) (+ a b)) (+ a b))) (/ (/ (* (* PI PI) PI) (* (* a a) a)) (* (* b b) b)))
605.0ms	(/ (/ (* (* PI PI) PI) (* (* a a) a)) (* (* b b) b))
503.0ms	(* (/ (* (* 1/2 1/2) 1/2) (* (* (+ a b) (+ a b)) (+ a b))) (/ (* (* (/ PI a) (/ PI a)) (/ PI a)) (* (* b b) b)))
375.0ms	(/ (* (* PI PI) PI) (* (* a a) a))

prune2.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes79.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.9s

9566×

body

valid