Details

sample81.0ms

Algorithm

intervals

Results

64.0ms

296×

body

valid

simplify453.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

453.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.5b

localize27.0ms

Local error

Found 4 expressions with local error:

9.0b	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
3.8b	(- (* b b) (* a a))
0.3b	(/ 1 (- (* b b) (* a a)))
0.2b	(* (/ PI 2) (/ 1 (- (* b b) (* a a))))

rewrite214.0ms

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

108.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
43.0ms	(* (/ PI 2) (/ 1 (- (* b b) (* a a))))
26.0ms	(/ 1 (- (* b b) (* a a)))
9.0ms	(- (* b b) (* a a))

series313.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
66.0ms	(* (/ PI 2) (/ 1 (- (* b b) (* a a))))
54.0ms	(/ 1 (- (* b b) (* a a)))
36.0ms	(- (* b b) (* a a))

simplify2.9m

Counts

521 → 543

Calls

521 calls:

Slowest

1.0s	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (fma (- (/ (cbrt 1) (sqrt b))) (/ (* (cbrt 1) (cbrt 1)) (sqrt b)) (* (/ (cbrt 1) (sqrt b)) (/ (* (cbrt 1) (cbrt 1)) (sqrt b)))))
912.0ms	(* (fma (- (/ 1 b)) 1 (* (/ 1 b) 1)) (* (/ PI 2) (/ 1 (- (* b b) (* a a)))))
897.0ms	(* (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)))))
834.0ms	(+ (+ (log (/ PI 2)) (log (/ 1 (- (* b b) (* a a))))) (log (- (/ 1 a) (/ 1 b))))
820.0ms	(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (fma (- (/ 1 b)) 1 (* (/ 1 b) 1)))

prune7.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite67.0ms

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

48.0ms	(/ (/ PI (+ b a)) (* 2 (* a b)))
17.0ms	(/ PI (+ b a))

series187.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

121.0ms	(/ (/ PI (+ b a)) (* 2 (* a b)))
66.0ms	(/ PI (+ b a))

simplify8.3s

Counts

105 → 105

Calls

105 calls:

Slowest

614.0ms	(/ (/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a))) (* (* (* 2 2) 2) (* (* (* a a) a) (* (* b b) b))))
574.0ms	(/ (/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a))) (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))))
491.0ms	(- (- (log PI) (log (+ b a))) (log (* 2 (* a b))))
483.0ms	(- (log (/ PI (+ b a))) (+ (log 2) (log (* a b))))
427.0ms	(/ (/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a))) (* (* (* 2 2) 2) (* (* (* a b) (* a b)) (* a b))))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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)))

rewrite67.0ms

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

28.0ms	(/ (/ 1 (/ (+ b a) PI)) (* 2 (* a b)))
17.0ms	(/ (+ b a) PI)
16.0ms	(/ 1 (/ (+ b a) PI))

series256.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

99.0ms	(/ (/ 1 (/ (+ b a) PI)) (* 2 (* a b)))
89.0ms	(/ (+ b a) PI)
67.0ms	(/ 1 (/ (+ b a) PI))

simplify42.1s

Counts

350 → 287

Calls

350 calls:

Slowest

956.0ms	(/ (* (* (/ 1 (/ (+ b a) PI)) (/ 1 (/ (+ b a) PI))) (/ 1 (/ (+ b a) PI))) (* (* (* 2 2) 2) (* (* (* a a) a) (* (* b b) b))))
928.0ms	(- (- (- (log (+ b a)) (log PI))) (+ (log 2) (+ (log a) (log b))))
901.0ms	(/ (* (* (/ 1 (/ (+ b a) PI)) (/ 1 (/ (+ b a) PI))) (/ 1 (/ (+ b a) PI))) (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))))
874.0ms	(/ (/ 1 (/ (cbrt (+ b a)) (cbrt PI))) (* a b))
764.0ms	(/ (* (* (/ 1 (/ (+ b a) PI)) (/ 1 (/ (+ b a) PI))) (/ 1 (/ (+ b a) PI))) (* (* (* 2 2) 2) (* (* (* a b) (* a b)) (* a b))))

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 3 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

294×	`times-frac`
172×	`*-un-lft-identity`
116×	`add-sqr-sqrt` `add-cube-cbrt`
76×	`add-exp-log`
46×	`add-cbrt-cube`
41×	`div-exp`
30×	`div-inv`
28×	`distribute-lft-out`
22×	`cbrt-undiv` `associate-/l*`
19×	`associate-/r/`
15×	`prod-exp`
14×	`associate-/r*`
9×	`flip3-+` `cbrt-unprod` `flip-+`
5×	`rec-exp` `1-exp`
4×	`pow1`
3×	`expm1-log1p-u` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `inv-pow` `associate-/l/`

Counts

3 → 256

Calls

3 calls:

Slowest

33.0ms	(/ (* 2 (* a b)) PI)
26.0ms	(/ (/ 1 (+ b a)) (/ (* 2 (* a b)) PI))
13.0ms	(/ 1 (+ b a))

series216.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

101.0ms	(/ (/ 1 (+ b a)) (/ (* 2 (* a b)) PI))
63.0ms	(/ (* 2 (* a b)) PI)
51.0ms	(/ 1 (+ b a))

simplify56.6s

Counts

358 → 265

Calls

358 calls:

Slowest

854.0ms	(/ (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (/ (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))) (* (* PI PI) PI)))
820.0ms	(/ (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (/ (* (* (* 2 2) 2) (* (* (* a a) a) (* (* b b) b))) (* (* PI PI) PI)))
781.0ms	(/ (* (* (/ 1 (+ b a)) (/ 1 (+ b a))) (/ 1 (+ b a))) (/ (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))) (* (* PI PI) PI)))
772.0ms	(/ (* (* (/ 1 (+ b a)) (/ 1 (+ b a))) (/ 1 (+ b a))) (/ (* (* (* 2 2) 2) (* (* (* a b) (* a b)) (* a b))) (* (* PI PI) PI)))
741.0ms	(/ (/ 1 (+ (pow b 3) (pow a 3))) (/ 2 (sqrt PI)))

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes118.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.8s

9653×

body

valid