Details

Time bar (total: 9.9m)

sample62.0ms

Algorithm
intervals
Results
48.0ms306×body80valid

simplify442.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
442.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize49.0ms

Local error

Found 4 expressions with local error:

5.0b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
4.0b
(- (* b b) (* a a))
4.0b
(- (* b b) (* a a))
3.4b
(/ (/ PI (- (* b b) (* a a))) a)

rewrite66.0ms

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
29.0ms
(/ (/ PI (- (* b b) (* a a))) a)
17.0ms
(- (* b b) (* a a))
16.0ms
(- (* b b) (* a a))
2.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series292.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
105.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
84.0ms
(/ (/ PI (- (* b b) (* a a))) a)
55.0ms
(- (* b b) (* a a))
48.0ms
(- (* b b) (* a a))

simplify20.9s

Counts
152 → 152
Calls
152 calls:
Slowest
746.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a))))) (sqrt a))
580.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
496.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
373.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (sqrt a))
316.0ms
(/ (+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a)))) (cbrt a))

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.3b

localize61.0ms

Local error

Found 4 expressions with local error:

5.0b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
4.0b
(- (* b b) (* a a))
0.9b
(/ PI (- (* b b) (* a a)))
0.2b
(/ PI (- b a))

rewrite44.0ms

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
19.0ms
(/ PI (- (* b b) (* a a)))
15.0ms
(/ PI (- b a))
8.0ms
(- (* b b) (* a a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series278.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
59.0ms
(- (* b b) (* a a))
57.0ms
(/ PI (- (* b b) (* a a)))
48.0ms
(/ PI (- b a))

simplify4.4s

Counts
92 → 117
Calls
92 calls:
Slowest
301.0ms
(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
220.0ms
(/ 1 (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))
203.0ms
(/ (exp (* b b)) (exp (* a a)))
199.0ms
(/ (sqrt PI) (- (* b b) (* a a)))
180.0ms
(/ (sqrt PI) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize60.0ms

Local error

Found 4 expressions with local error:

5.0b
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
0.2b
(/ PI (- b a))
0.2b
(/ PI (- b a))
0.2b
(/ (/ 1 (+ b a)) (/ a (/ PI (- b a))))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
4134×times-frac
2279×*-un-lft-identity
1865×add-sqr-sqrt
1507×add-cube-cbrt
276×associate-/r/
207×distribute-lft-out
179×distribute-lft-out-- difference-of-squares
148×div-inv
78×associate-/r*
69×flip3-+ flip-+
59×flip3-- flip--
47×add-exp-log
32×div-exp
29×add-cbrt-cube
24×associate-/l*
17×cbrt-undiv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg 1-exp
1×fma-udef associate-/l/
Counts
4 → 1434
Calls
4 calls:
Slowest
27.0ms
(/ (/ 1 (+ b a)) (/ a (/ PI (- b a))))
23.0ms
(/ PI (- b a))
16.0ms
(/ PI (- b a))
1.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
176.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
102.0ms
(/ (/ 1 (+ b a)) (/ a (/ PI (- b a))))
63.0ms
(/ PI (- b a))
59.0ms
(/ PI (- b a))

simplify9.2m

Counts
2645 → 1446
Calls
2645 calls:
Slowest
1.7s
(/ (/ (cbrt 1) (+ b a)) (/ a (+ b a)))
1.3s
(/ (/ 1 (+ b a)) (/ a (+ b a)))
1.3s
(/ (/ (cbrt 1) (+ b a)) (/ a (+ b a)))
1.2s
(/ (/ (sqrt 1) (+ b a)) (/ a (+ b a)))
1.2s
(/ (/ 1 1) (/ 1 (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- b a)) (cbrt (- b a))))))

prune14.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize35.0ms

Local error

Found 4 expressions with local error:

5.0b
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (* (/ (/ 1 (+ b a)) a) (/ PI (- b a))))
0.2b
(/ PI (- b a))
0.2b
(/ PI (- b a))
0.2b
(/ (/ 1 (+ b a)) a)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
115×*-un-lft-identity
91×add-sqr-sqrt
75×add-cube-cbrt
24×associate-/l*
17×add-exp-log
13×associate-/r* add-cbrt-cube
12×associate-/r/ distribute-lft-out
8×div-exp distribute-lft-out-- difference-of-squares
7×div-inv
5×cbrt-undiv
4×expm1-log1p-u pow1 flip3-+ flip-+ insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×flip3-- flip--
1×rec-exp 1-exp fma-udef associate-/l/
Counts
4 → 186
Calls
4 calls:
Slowest
14.0ms
(/ (/ 1 (+ b a)) a)
8.0ms
(/ 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))))

series232.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (* (/ (/ 1 (+ b a)) a) (/ PI (- b a))))
49.0ms
(/ PI (- b a))
44.0ms
(/ PI (- b a))
38.0ms
(/ (/ 1 (+ b a)) a)