Details

Time bar (total: 1.0m)

sample69.0ms

Algorithm
intervals
Results
55.0ms311×body80valid

simplify423.0ms

Calls
1 calls:
Slowest
423.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize27.0ms

Local error

Found 4 expressions with local error:

5.1b
(/ (/ PI (- (* b b) (* a a))) a)
4.4b
(- (* b b) (* a a))
4.4b
(- (* b b) (* a a))
4.1b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
55×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-/l*
14×difference-of-squares
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 associate-/r* div-exp
2×sub-neg fma-neg diff-log prod-diff
1×clear-num frac-2neg fma-udef associate-/l/
Calls
4 calls:
Slowest
50.0ms
(/ (/ PI (- (* b b) (* a a))) a)
16.0ms
(- (* b b) (* a a))
16.0ms
(- (* b b) (* a a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series302.0ms

Calls
4 calls:
Slowest
114.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
99.0ms
(/ (/ PI (- (* b b) (* a a))) a)
48.0ms
(- (* b b) (* a a))
41.0ms
(- (* b b) (* a a))

simplify20.7s

Calls
152 calls:
Slowest
660.0ms
(/ (+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a)))) a)
532.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
478.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (sqrt a))
460.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
363.0ms
(/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a))))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize33.0ms

Local error

Found 4 expressions with local error:

4.4b
(- (* b b) (* a a))
4.1b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
0.4b
(/ PI (- (* b b) (* a a)))
0.3b
(/ PI (- b a))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt *-un-lft-identity
27×times-frac
23×add-cube-cbrt
9×associate-/r* difference-of-squares
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--
3×flip3-- flip--
2×cbrt-undiv clear-num frac-2neg div-exp div-inv
1×sub-neg fma-neg diff-log prod-diff fma-udef
Calls
4 calls:
Slowest
13.0ms
(/ PI (- b a))
10.0ms
(/ PI (- (* b b) (* a a)))
8.0ms
(- (* b b) (* a a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))

series280.0ms

Calls
4 calls:
Slowest
129.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
68.0ms
(/ PI (- b a))
45.0ms
(/ PI (- (* b b) (* a a)))
38.0ms
(- (* b b) (* a a))

simplify4.4s

Calls
92 calls:
Slowest
353.0ms
(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
239.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))
197.0ms
(/ (exp (* b b)) (exp (* a a)))
188.0ms
(/ (cbrt PI) (- (* b b) (* a a)))
185.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize45.0ms

Local error

Found 4 expressions with local error:

4.1b
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
0.3b
(/ PI (+ b a))
0.3b
(/ PI (- b a))
0.2b
(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
136×add-sqr-sqrt
123×*-un-lft-identity
80×add-cube-cbrt
67×associate-*r*
47×add-exp-log
29×add-cbrt-cube
20×div-exp
18×associate-*l*
13×distribute-lft-out-- difference-of-squares
12×prod-exp associate-/r/
11×cbrt-undiv
9×associate-/r* unswap-sqr
7×div-inv distribute-lft-out
6×pow1 cbrt-unprod associate-/l*
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip-- add-log-exp
3×rec-exp 1-exp
2×clear-num frac-2neg flip3-+ flip-+
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative fma-udef
Calls
4 calls:
Slowest
71.0ms
(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))
8.0ms
(/ PI (- b a))
8.0ms
(/ PI (+ b a))
0.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))

series409.0ms

Calls
4 calls:
Slowest
152.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
127.0ms
(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))
70.0ms
(/ PI (+ b a))
61.0ms
(/ PI (- b a))

simplify13.9s

Calls
210 calls:
Slowest
621.0ms
(* (/ 1 (sqrt (+ b a))) (/ (/ (sqrt PI) (sqrt (- b a))) (sqrt a)))
563.0ms
(* (/ 1 (sqrt (+ b a))) (/ (/ (sqrt PI) (sqrt (- b a))) (sqrt a)))
524.0ms
(* (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (/ (/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a))) (* (* a a) a)))
497.0ms
(+ (log (/ 1 (+ b a))) (log (/ (/ PI (- b a)) a)))
433.0ms
(* (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (/ (* (* (/ PI (- b a)) (/ PI (- b a))) (/ PI (- b a))) (* (* a a) a)))

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

localize67.0ms

Local error

Found 4 expressions with local error:

4.1b
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (pow (/ (/ (/ PI a) (- b a)) (+ b a)) 1))
0.3b
(/ PI a)
0.3b
(/ PI (+ b a))
0.2b
(/ (/ PI a) (- b a))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
113×*-un-lft-identity
105×add-sqr-sqrt
77×add-cube-cbrt
19×associate-/l*
14×distribute-lft-out-- difference-of-squares
13×add-cbrt-cube add-exp-log
12×associate-/r*
9×div-inv
5×cbrt-undiv div-exp
4×expm1-log1p-u pow1 associate-/r/ insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
3×clear-num frac-2neg
1×flip3-+ flip3-- flip-+ fma-udef flip-- associate-/l/
Calls
4 calls:
Slowest
23.0ms
(/ (/ PI a) (- b a))
15.0ms
(/ PI (+ b a))
8.0ms
(/ PI a)
1.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (pow (/ (/ (/ PI a) (- b a)) (+ b a)) 1))

series354.0ms

Calls
4 calls:
Slowest
160.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (pow (/ (/ (/ PI a) (- b a)) (+ b a)) 1))
102.0ms
(/ (/ PI a) (- b a))
63.0ms
(/ PI (+ b a))
29.0ms
(/ PI a)

simplify7.7s

Calls
222 calls:
Slowest
772.0ms
(/ (* (* PI PI) PI) (* (* a a) a))
450.0ms
(/ (* (* (/ PI a) (/ PI a)) (/ PI a)) (* (* (- b a) (- b a)) (- b a)))
411.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) (* (cbrt a) (cbrt a))) (* (cbrt (- b a)) (cbrt (- b a))))
314.0ms
(/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a)))
159.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) (* (cbrt a) (cbrt a))) (+ (sqrt b) (sqrt a)))

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

regimes316.0ms

Accuracy

0% (0.2b remaining)

Error of 4.5b against oracle of 4.3b and baseline of 4.5b

bsearch5.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.9s9564×body80valid