Details

Time bar (total: 51.1s)

sample58.0ms

Algorithm
intervals
Results
46.0ms305×body80valid

simplify459.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
459.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize28.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (/ PI (- (* b b) (* a a))) a)
5.2b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
4.8b
(- (* b b) (* a a))
4.8b
(- (* b b) (* a a))

rewrite70.0ms

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/
Counts
4 → 140
Calls
4 calls:
Slowest
50.0ms
(/ (/ PI (- (* b b) (* a a))) a)
8.0ms
(- (* b b) (* a a))
8.0ms
(- (* b b) (* a a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
90.0ms
(/ (/ PI (- (* b b) (* a a))) a)
45.0ms
(- (* b b) (* a a))
43.0ms
(- (* b b) (* a a))

simplify20.1s

Counts
152 → 152
Calls
152 calls:
Slowest
725.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (sqrt a))
536.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
440.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
394.0ms
(/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a))))
339.0ms
(/ (/ PI (- (* b b) (* a a))) (cbrt a))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize41.0ms

Local error

Found 4 expressions with local error:

5.2b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
4.8b
(- (* b b) (* a a))
0.3b
(/ PI (- (* b b) (* a a)))
0.3b
(/ PI (- b a))

rewrite48.0ms

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
Counts
4 → 105
Calls
4 calls:
Slowest
24.0ms
(- (* b b) (* a a))
15.0ms
(/ PI (- (* b b) (* a a)))
8.0ms
(/ PI (- b a))
1.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series271.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
50.0ms
(/ PI (- (* b b) (* a a)))
47.0ms
(/ PI (- b a))
33.0ms
(- (* b b) (* a a))

simplify4.1s

Counts
92 → 117
Calls
92 calls:
Slowest
312.0ms
(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
191.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))
174.0ms
(/ (* (cbrt PI) (cbrt PI)) (sqrt (- (* b b) (* a a))))
173.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))
173.0ms
(/ (cbrt PI) (cbrt (- (* b b) (* a a))))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize28.0ms

Local error

Found 4 expressions with local error:

5.2b
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
0.3b
(/ PI (- b a))
0.3b
(/ PI (- b a))
0.2b
(/ a (/ PI (- b a)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
153×times-frac
122×add-sqr-sqrt *-un-lft-identity
82×add-cube-cbrt
31×associate-/r*
20×distribute-lft-out-- difference-of-squares
13×add-cbrt-cube add-exp-log associate-/r/
9×associate-/l*
7×div-inv
6×flip3-- flip--
5×cbrt-undiv div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef
Counts
4 → 196
Calls
4 calls:
Slowest
27.0ms
(/ a (/ PI (- b a)))
12.0ms
(/ PI (- b a))
8.0ms
(/ PI (- b a))
0.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series418.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
102.0ms
(/ a (/ PI (- b a)))
77.0ms
(/ PI (- b a))
66.0ms
(/ PI (- b a))

simplify12.6s

Counts
248 → 208
Calls
248 calls:
Slowest
528.0ms
(/ (* (* a a) a) (* (* (/ PI (- b a)) (/ PI (- b a))) (/ PI (- b a))))
482.0ms
(/ (* (cbrt a) (cbrt a)) (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- b a)) (cbrt (- b a)))))
467.0ms
(/ 1 (/ PI (- (* b b) (* a a))))
442.0ms
(/ (sqrt a) (/ PI (- (* b b) (* a a))))
250.0ms
(/ (* (cbrt a) (cbrt a)) (/ (* (cbrt PI) (cbrt PI)) (+ (sqrt b) (sqrt a))))

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize86.0ms

Local error

Found 4 expressions with local error:

5.2b
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ 1 (sqrt PI)) (/ a (/ (sqrt PI) (- b a))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)
0.3b
(/ (sqrt PI) (- b a))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
39×*-un-lft-identity
30×times-frac
25×add-cube-cbrt
24×sqrt-prod
7×distribute-lft-out-- difference-of-squares
6×pow1 add-cbrt-cube add-exp-log associate-/l*
5×associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv clear-num frac-2neg flip3-- div-exp fma-udef div-inv flip--
Counts
4 → 101
Calls
4 calls:
Slowest
9.0ms
(/ (sqrt PI) (- b a))
2.0ms
(sqrt PI)
1.0ms
(sqrt PI)
1.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ 1 (sqrt PI)) (/ a (/ (sqrt PI) (- b a))))))

series300.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
155.0ms
(/ (sqrt PI) (- b a))
145.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ 1 (sqrt PI)) (/ a (/ (sqrt PI) (- b a))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.6s

Counts
90 → 109
Calls
90 calls:
Slowest
196.0ms
(/ (fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ 1 (sqrt PI)) (/ a (/ (sqrt PI) (- b a)))))) 2)
155.0ms
(/ (* (* (sqrt PI) (sqrt PI)) (sqrt PI)) (* (* (- b a) (- b a)) (- b a)))
154.0ms
(/ (fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ 1 (sqrt PI)) (/ a (/ (sqrt PI) (- b a)))))) 2)
72.0ms
(/ (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (* (cbrt (- b a)) (cbrt (- b a))))
46.0ms
(+ (* b b) (+ (* a a) (* b a)))

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

regimes287.0ms

Accuracy

0% (0.2b remaining)

Error of 4.8b against oracle of 4.6b and baseline of 4.8b

bsearch8.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.9s9595×body80valid