Details

Time bar (total: 1.0m)

sample88.0ms

Algorithm
intervals
Results
73.0ms303×body80valid

simplify478.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
477.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

localize54.0ms

Local error

Found 4 expressions with local error:

5.4b
(/ (/ PI (- (* b b) (* a a))) a)
3.5b
(- (* b b) (* a a))
3.5b
(- (* b b) (* a a))
3.4b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

rewrite56.0ms

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
33.0ms
(/ (/ PI (- (* b b) (* a a))) a)
11.0ms
(- (* 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))

series710.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
435.0ms
(- (* b b) (* a a))
115.0ms
(/ (/ PI (- (* b b) (* a a))) a)
114.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
45.0ms
(- (* b b) (* a a))

simplify20.6s

Counts
152 → 152
Calls
152 calls:
Slowest
481.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
475.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
390.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) 1)
381.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (sqrt a))
344.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a))))) (sqrt a))

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize61.0ms

Local error

Found 4 expressions with local error:

3.5b
(- (* b b) (* a a))
3.4b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
0.6b
(/ PI (- (* b b) (* a a)))
0.2b
(/ PI (- b a))

rewrite29.0ms

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
11.0ms
(/ PI (- (* b b) (* a a)))
8.0ms
(- (* b b) (* a a))
8.0ms
(/ PI (- b a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
79.0ms
(/ PI (- (* b b) (* a a)))
79.0ms
(/ PI (- b a))
57.0ms
(- (* b b) (* a a))

simplify4.2s

Counts
92 → 117
Calls
92 calls:
Slowest
291.0ms
(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
211.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))
205.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))
201.0ms
(/ (sqrt PI) (cbrt (- (* b b) (* a a))))
198.0ms
(/ PI (cbrt (- (* b b) (* a a))))

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize59.0ms

Local error

Found 4 expressions with local error:

3.4b
(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))

rewrite119.0ms

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
70.0ms
(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))
23.0ms
(/ PI (- b a))
18.0ms
(/ PI (- b a))
1.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
106.0ms
(* (/ 1 (+ b a)) (/ (/ PI (- b a)) a))
76.0ms
(/ PI (- b a))
68.0ms
(/ PI (- b a))

simplify14.2s

Counts
217 → 230
Calls
217 calls:
Slowest
572.0ms
(* (/ 1 (sqrt (+ b a))) (/ (/ (sqrt PI) (sqrt (- b a))) (sqrt a)))
544.0ms
(* (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (/ (* (* (/ PI (- b a)) (/ PI (- b a))) (/ PI (- b a))) (* (* a a) a)))
540.0ms
(* (/ 1 (sqrt (+ b a))) (/ (/ (sqrt PI) (sqrt (- b a))) (sqrt a)))
497.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))
481.0ms
(* (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (/ (/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a))) (* (* a a) a)))

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.4b

localize75.0ms

Local error

Found 4 expressions with local error:

3.4b
(fma (* (/ 1 (+ b a)) (/ 1 (/ (- b a) PI))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
0.3b
(/ 1 (/ (- b a) PI))
0.2b
(/ PI (- b a))
0.2b
(/ (- b a) PI)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
120×add-sqr-sqrt *-un-lft-identity
80×add-cube-cbrt
27×associate-/r*
20×distribute-lft-out-- difference-of-squares
19×add-exp-log
13×add-cbrt-cube
11×associate-/l*
9×div-exp
7×div-inv
5×pow1 cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-/r/
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×div-sub fma-udef pow-flip inv-pow
Counts
4 → 195
Calls
4 calls:
Slowest
17.0ms
(/ (- b a) PI)
10.0ms
(/ 1 (/ (- b a) PI))
8.0ms
(/ PI (- b a))
0.0ms
(fma (* (/ 1 (+ b a)) (/ 1 (/ (- b a) PI))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(fma (* (/ 1 (+ b a)) (/ 1 (/ (- b a) PI))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
84.0ms
(/ (- b a) PI)
64.0ms
(/ PI (- b a))
63.0ms
(/ 1 (/ (- b a) PI))

simplify9.3s

Counts
235 → 207
Calls
235 calls:
Slowest
379.0ms
(/ (* (* 1 1) 1) (/ (* (* (- b a) (- b a)) (- b a)) (* (* PI PI) PI)))
354.0ms
(/ (sqrt 1) (/ (* (cbrt (- b a)) (cbrt (- b a))) (* (cbrt PI) (cbrt PI))))
308.0ms
(/ (* (* 1 1) 1) (* (* (/ (- b a) PI) (/ (- b a) PI)) (/ (- b a) PI)))
274.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- b a)) (cbrt (- b a))) (* (cbrt PI) (cbrt PI))))
274.0ms
(/ (* (* (- b a) (- b a)) (- b a)) (* (* PI PI) PI))

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

regimes293.0ms

Accuracy

0% (0.2b remaining)

Error of 4.4b against oracle of 4.2b and baseline of 4.4b

bsearch5.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.3s9642×body80valid