Details

Time bar (total: 1.0m)

sample84.0ms

Algorithm
intervals
Results
65.0ms312×body80valid

simplify477.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
477.0ms
(* (* (/ 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: 15.4b

localize24.0ms

Local error

Found 4 expressions with local error:

5.5b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
5.0b
(- (* b b) (* a a))
5.0b
(- (* b b) (* a a))
4.2b
(/ (/ PI (- (* b b) (* a a))) a)

rewrite64.0ms

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
31.0ms
(/ (/ PI (- (* b b) (* a a))) a)
15.0ms
(- (* b b) (* a a))
15.0ms
(- (* b b) (* a a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series315.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(/ (/ PI (- (* b b) (* a a))) a)
98.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
57.0ms
(- (* b b) (* a a))
43.0ms
(- (* b b) (* a a))

simplify21.5s

Counts
152 → 152
Calls
152 calls:
Slowest
711.0ms
(- (- (log PI) (log (- (* b b) (* a a)))) (log a))
517.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
515.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
416.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (sqrt a))
405.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) 1)

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.6b

localize57.0ms

Local error

Found 4 expressions with local error:

5.5b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
5.0b
(- (* b b) (* a a))
0.4b
(/ PI (- (* b b) (* a a)))
0.2b
(/ PI (- b a))

rewrite32.0ms

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
15.0ms
(/ PI (- (* b b) (* a a)))
8.0ms
(- (* b b) (* a a))
7.0ms
(/ PI (- b a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
76.0ms
(/ PI (- b a))
69.0ms
(/ PI (- (* b b) (* a a)))
39.0ms
(- (* b b) (* a a))

simplify4.1s

Counts
92 → 117
Calls
92 calls:
Slowest
324.0ms
(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
242.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))
182.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))
170.0ms
(- (log PI) (log (- (* b b) (* a a))))
165.0ms
(/ (sqrt PI) (cbrt (- (* b b) (* a a))))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize66.0ms

Local error

Found 4 expressions with local error:

5.5b
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
0.2b
(/ PI (- b a))
0.2b
(/ PI (- b a))
0.2b
(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
145×add-sqr-sqrt
124×*-un-lft-identity
81×add-cube-cbrt
67×associate-*r*
47×add-exp-log
29×add-cbrt-cube
20×div-exp
18×associate-*l*
17×distribute-lft-out-- difference-of-squares
12×prod-exp associate-/r/
11×cbrt-undiv
10×associate-/r*
9×unswap-sqr
7×div-inv
6×pow1 cbrt-unprod associate-/l*
5×flip3-- flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp distribute-lft-out
2×clear-num frac-2neg
1×frac-times flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+ fma-udef
Counts
4 → 218
Calls
4 calls:
Slowest
53.0ms
(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))
16.0ms
(/ PI (- b a))
16.0ms
(/ PI (- b a))
1.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
115.0ms
(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))
79.0ms
(/ PI (- b a))
68.0ms
(/ PI (- b a))

simplify14.5s

Counts
217 → 230
Calls
217 calls:
Slowest
698.0ms
(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))
583.0ms
(* (/ 1 (sqrt (+ b a))) (/ (/ (sqrt PI) (sqrt (- b a))) (sqrt a)))
573.0ms
(* (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (/ (/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a))) (* (* a a) a)))
548.0ms
(* (/ 1 (sqrt (+ b a))) (/ (/ (sqrt PI) (sqrt (- b a))) (sqrt a)))
485.0ms
(* (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (/ (* (* (/ PI (- b a)) (/ PI (- b a))) (/ PI (- b a))) (* (* a a) a)))

prune2.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize60.0ms

Local error

Found 4 expressions with local error:

5.5b
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ PI (- b a)) (* (+ b a) a)))
0.2b
(/ PI (- b a))
0.2b
(/ PI (- b a))
0.2b
(/ (/ PI (- b a)) (* (+ b a) a))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
81×times-frac
70×add-sqr-sqrt *-un-lft-identity
42×add-cube-cbrt
27×associate-/l*
20×add-cbrt-cube add-exp-log
14×distribute-lft-out-- difference-of-squares
11×associate-/r*
10×associate-/r/
8×cbrt-undiv div-exp
5×div-inv
4×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip-- add-log-exp
3×clear-num frac-2neg
2×associate-*l/ prod-exp cbrt-unprod
1×flip3-+ flip-+ fma-udef associate-/l/
Counts
4 → 158
Calls
4 calls:
Slowest
39.0ms
(/ (/ PI (- b a)) (* (+ b a) a))
23.0ms
(/ PI (- b a))
16.0ms
(/ PI (- b a))
1.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ PI (- b a)) (* (+ b a) a)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ PI (- b a)) (* (+ b a) a)))
100.0ms
(/ (/ PI (- b a)) (* (+ b a) a))
62.0ms
(/ PI (- b a))
46.0ms
(/ PI (- b a))

simplify7.9s

Counts
165 → 170
Calls
165 calls:
Slowest
507.0ms
(/ (/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a))) (* (* (* (+ b a) (+ b a)) (+ b a)) (* (* a a) a)))
460.0ms
(/ (/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a))) (* (* (* (+ b a) a) (* (+ b a) a)) (* (+ b a) a)))
454.0ms
(/ (/ PI (- (* b b) (* a a))) (+ b a))
375.0ms
(/ (* (* (/ PI (- b a)) (/ PI (- b a))) (/ PI (- b a))) (* (* (* (+ b a) a) (* (+ b a) a)) (* (+ b a) a)))
330.0ms
(- (- (log PI) (log (- b a))) (+ (log (+ b a)) (log a)))

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.4b

regimes304.0ms

Accuracy

0% (0.2b remaining)

Error of 4.8b against oracle of 4.5b and baseline of 4.8b

bsearch4.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
2.2s9555×body80valid