Details

sample97.0ms

Algorithm

intervals

Results

82.0ms

307×

body

valid

simplify465.0ms

Calls

1 calls:

Slowest

465.0ms

(* (* (/ 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: 12.8b

localize34.0ms

Local error

Found 4 expressions with local error:

4.5b	(- (* b b) (* a a))
4.5b	(- (* b b) (* a a))
3.8b	(/ (/ PI (- (* b b) (* a a))) a)
3.4b	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

1444×	`add-sqr-sqrt`
750×	`*-un-lft-identity`
711×	`times-frac`
570×	`add-cube-cbrt`
450×	`prod-diff`
375×	`difference-of-squares`
366×	`swap-sqr`
246×	`associate-l`
212×	`*-commutative` `unswap-sqr`
186×	`associate-r`
108×	`associate-/l*`
75×	`distribute-lft-out--`
39×	`associate-/l/`
36×	`associate-/r*`
30×	`fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp`
2×	`clear-num` `sub-neg` `frac-2neg` `diff-log`
1×	`fma-udef`

Calls

4 calls:

Slowest

88.0ms	(/ (/ PI (- (* b b) (* a a))) a)
45.0ms	(- (* b b) (* a a))
35.0ms	(- (* b b) (* a a))
0.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series306.0ms

Calls

4 calls:

Slowest

99.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
81.0ms	(/ (/ PI (- (* b b) (* a a))) a)
81.0ms	(- (* b b) (* a a))
45.0ms	(- (* b b) (* a a))

simplify2.5m

Calls

1823 calls:

Slowest

632.0ms	(/ (/ (sqrt PI) (- (* b b) (* a a))) (sqrt a))
556.0ms	(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
547.0ms	(fma (- (cbrt (* a a))) (* (cbrt (* a a)) (cbrt (* a a))) (* (cbrt (* a a)) (* (cbrt (* a a)) (cbrt (* a a)))))
506.0ms	(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
445.0ms	(fma (* b (sqrt b)) (sqrt b) (- (* (* a a) (* 1 1))))

prune13.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

localize69.0ms

Local error

Found 4 expressions with local error:

4.5b	(- (* b b) (* a a))
3.4b	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (+ b a)) (* a (- b a))))
0.9b	(/ PI (- (* b b) (* a a)))
0.3b	(/ PI (+ b a))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

518×	`add-sqr-sqrt`
274×	`*-un-lft-identity`
225×	`prod-diff`
206×	`add-cube-cbrt`
153×	`swap-sqr`
125×	`difference-of-squares`
113×	`associate-l`
111×	`times-frac`
93×	`associate-r`
81×	`*-commutative` `unswap-sqr`
37×	`associate-/r*`
25×	`distribute-lft-out--`
15×	`fma-neg`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `associate-/r/` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--`
1×	`sub-neg` `flip3-+` `diff-log` `flip-+` `fma-udef`

Calls

4 calls:

Slowest

66.0ms	(- (* b b) (* a a))
34.0ms	(/ PI (- (* b b) (* a a)))
16.0ms	(/ PI (+ b a))
0.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (+ b a)) (* a (- b a))))

series295.0ms

Calls

4 calls:

Slowest

134.0ms	(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (+ b a)) (* a (- b a))))
57.0ms	(/ PI (- (* b b) (* a a)))
55.0ms	(- (* b b) (* a a))
49.0ms	(/ PI (+ b a))

simplify52.4s

Calls

801 calls:

Slowest

658.0ms	(fma (sqrt b) (* (sqrt b) b) (- (* (* (cbrt a) (cbrt a)) (* (* (cbrt a) (cbrt a)) (* (cbrt a) (cbrt a))))))
386.0ms	(fma 1 (* b b) (- (* (* (cbrt a) (cbrt a)) (* (* (cbrt a) (cbrt a)) (* (cbrt a) (cbrt a))))))
374.0ms	(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
371.0ms	(fma (sqrt (* b b)) (sqrt (* b b)) (- (* (* (cbrt a) (cbrt a)) (* (* (cbrt a) (cbrt a)) (* (cbrt a) (cbrt a))))))
335.0ms	(/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a)))

prune6.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.3b

localize37.0ms

Local error

Found 4 expressions with local error:

3.4b	(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ PI (+ b a)) (* a (- b a))))
0.3b	(/ PI (+ b a))
0.3b	(/ PI (+ b a))
0.1b	(/ (/ PI (+ b a)) (* a (- b a)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

456×	`times-frac`
347×	`*-un-lft-identity`
277×	`add-sqr-sqrt`
201×	`add-cube-cbrt`
95×	`associate-r`
57×	`associate-l`
54×	`distribute-lft-out`
36×	`associate-/r/`
27×	`associate-/l*`
26×	`associate-/r*`
20×	`add-cbrt-cube` `add-exp-log`
19×	`*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
18×	`div-inv`
17×	`flip3-+` `flip-+`
10×	`associate-/l/`
8×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `associate-*r/` `cbrt-unprod`
1×	`flip3--` `fma-udef` `flip--`

Calls

4 calls:

Slowest

55.0ms	(/ (/ PI (+ b a)) (* a (- b a)))
14.0ms	(/ PI (+ b a))
9.0ms	(/ PI (+ b a))
0.0ms	(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ PI (+ b a)) (* a (- b a))))

series355.0ms

Calls

4 calls:

Slowest

127.0ms	(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ PI (+ b a)) (* a (- b a))))
102.0ms	(/ (/ PI (+ b a)) (* a (- b a)))
70.0ms	(/ PI (+ b a))
55.0ms	(/ PI (+ b a))

simplify57.0s

Calls

630 calls:

Slowest

760.0ms	(/ (/ PI (- (* b b) (* a a))) (sqrt (* a (- b a))))
581.0ms	(/ (/ (cbrt PI) (+ b a)) (* a (- b a)))
494.0ms	(/ (/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a))) (* (* (* a a) a) (* (* (- b a) (- b a)) (- b a))))
480.0ms	(/ (/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a))) (* (* (* a (- b a)) (* a (- b a))) (* a (- b a))))
454.0ms	(/ (/ PI (- (* b b) (* a a))) (* a (* (cbrt (- b a)) (cbrt (- b a)))))

prune5.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize34.0ms

Local error

Found 4 expressions with local error:

3.4b	(fma (/ (/ 1 (/ (+ b a) PI)) (- b a)) (/ -1 b) (/ (/ PI (+ b a)) (* a (- b a))))
0.4b	(/ 1 (/ (+ b a) PI))
0.3b	(/ PI (+ b a))
0.3b	(/ (+ b a) PI)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
118×	`*-un-lft-identity`
73×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`associate-/r*`
22×	`distribute-lft-out`
19×	`add-exp-log`
16×	`associate-/l*`
14×	`associate-/r/`
13×	`add-cbrt-cube`
9×	`div-exp`
7×	`div-inv`
5×	`pow1` `cbrt-undiv` `clear-num`
4×	`expm1-log1p-u` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`flip3-+` `flip-+` `remove-double-div`
2×	`rec-exp` `1-exp`
1×	`fma-udef` `pow-flip` `inv-pow`

Calls

4 calls:

Slowest

35.0ms	(/ 1 (/ (+ b a) PI))
29.0ms	(/ (+ b a) PI)
16.0ms	(/ PI (+ b a))
0.0ms	(fma (/ (/ 1 (/ (+ b a) PI)) (- b a)) (/ -1 b) (/ (/ PI (+ b a)) (* a (- b a))))

series325.0ms

Calls

4 calls:

Slowest

143.0ms	(fma (/ (/ 1 (/ (+ b a) PI)) (- b a)) (/ -1 b) (/ (/ PI (+ b a)) (* a (- b a))))
84.0ms	(/ (+ b a) PI)
54.0ms	(/ 1 (/ (+ b a) PI))
44.0ms	(/ PI (+ b a))

simplify7.1s

Calls

212 calls:

Slowest

372.0ms	(* PI (+ (* b b) (- (* a a) (* b a))))
345.0ms	(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* PI PI) PI))
316.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (+ b a)) (cbrt (+ b a))) (* (cbrt PI) (cbrt PI))))
302.0ms	(/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a)))
272.0ms	(/ (sqrt 1) (/ (* (cbrt (+ b a)) (cbrt (+ b a))) (* (cbrt PI) (cbrt PI))))

prune2.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.3b

regimes279.0ms

Accuracy

0% (0.2b remaining)

Error of 4.8b against oracle of 4.7b and baseline of 4.8b

bsearch5.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.9s

9558×

body

valid