Details

Time bar (total: 51.3s)

sample65.0ms

Algorithm
intervals
Results
50.0ms321×body80valid

simplify406.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
406.0ms
(* (* (/ 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: 13.4b

localize24.0ms

Local error

Found 4 expressions with local error:

4.7b
(- (* b b) (* a a))
4.7b
(- (* b b) (* a a))
4.1b
(/ (/ PI (- (* b b) (* a a))) a)
4.0b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

rewrite47.0ms

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
27.0ms
(/ (/ PI (- (* b b) (* a a))) a)
9.0ms
(- (* 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))

series618.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
371.0ms
(- (* b b) (* a a))
103.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
103.0ms
(/ (/ PI (- (* b b) (* a a))) a)
41.0ms
(- (* b b) (* a a))

simplify20.3s

Counts
152 → 152
Calls
152 calls:
Slowest
565.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
488.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
374.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) 1)
370.0ms
(- (- (log PI) (log (- (* b b) (* a a)))) (log a))
348.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (sqrt a))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.3b

localize40.0ms

Local error

Found 4 expressions with local error:

4.7b
(- (* b b) (* a a))
4.0b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
0.5b
(/ PI (- (* b b) (* a a)))
0.2b
(/ PI (- b a))

rewrite37.0ms

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
12.0ms
(- (* b b) (* a a))
12.0ms
(/ PI (- b a))
11.0ms
(/ PI (- (* b b) (* a a)))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
66.0ms
(/ PI (- b a))
55.0ms
(/ PI (- (* b b) (* a a)))
47.0ms
(- (* b b) (* a a))

simplify4.0s

Counts
92 → 117
Calls
92 calls:
Slowest
251.0ms
(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
196.0ms
(/ 1 (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))
193.0ms
(- (log PI) (log (- (* b b) (* a a))))
184.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))
176.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
189×times-frac
180×*-un-lft-identity
136×add-sqr-sqrt
90×add-cube-cbrt
24×associate-/l*
23×distribute-lft-out-- difference-of-squares
22×distribute-lft-out
18×associate-/r/
14×associate-/r*
13×add-cbrt-cube add-exp-log
9×div-inv
7×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
2×flip3-- flip--
1×fma-udef associate-/l/
Counts
4 → 220
Calls
4 calls:
Slowest
17.0ms
(/ (/ PI (+ b a)) (- b a))
14.0ms
(/ PI (- b a))
8.0ms
(/ PI (+ b a))
1.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series357.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
94.0ms
(/ (/ PI (+ b a)) (- b a))
68.0ms
(/ PI (+ b a))
59.0ms
(/ PI (- b a))

simplify17.9s

Counts
294 → 232
Calls
294 calls:
Slowest
803.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (+ b a)) (cbrt (+ b a)))) (* (cbrt (- b a)) (cbrt (- b a))))
495.0ms
(/ (* (* (/ PI (+ b a)) (/ PI (+ b a))) (/ PI (+ b a))) (* (* (- b a) (- b a)) (- b a)))
414.0ms
(/ (/ PI (+ (pow b 3) (pow a 3))) (+ (sqrt b) (sqrt a)))
400.0ms
(/ (/ PI (- (* b b) (* a a))) 1)
394.0ms
(/ (/ PI (+ (pow b 3) (pow a 3))) 1)

prune3.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

localize66.0ms

Local error

Found 4 expressions with local error:

4.0b
(fma (/ PI (/ (- b a) (/ 1 (+ b a)))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
0.5b
(/ PI (/ (- b a) (/ 1 (+ b a))))
0.2b
(/ PI (- b a))
0.1b
(/ (/ 1 (+ b a)) (/ a (/ PI (- b a))))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
5004×times-frac
2857×*-un-lft-identity
2323×add-sqr-sqrt
1829×add-cube-cbrt
319×associate-/r/
267×distribute-lft-out
247×distribute-lft-out-- difference-of-squares
172×div-inv
168×associate-/r*
89×flip3-+ flip-+
60×add-exp-log
58×flip3-- flip--
42×div-exp
36×add-cbrt-cube
24×associate-/l*
22×cbrt-undiv
4×expm1-log1p-u pow1 rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef associate-/l/
Counts
4 → 1799
Calls
4 calls:
Slowest
37.0ms
(/ (/ 1 (+ b a)) (/ a (/ PI (- b a))))
32.0ms
(/ PI (/ (- b a) (/ 1 (+ b a))))
16.0ms
(/ PI (- b a))
1.0ms
(fma (/ PI (/ (- b a) (/ 1 (+ b a)))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(fma (/ PI (/ (- b a) (/ 1 (+ b a)))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
105.0ms
(/ (/ 1 (+ b a)) (/ a (/ PI (- b a))))
71.0ms
(/ PI (- b a))
64.0ms
(/ PI (/ (- b a) (/ 1 (+ b a))))