Details

Time bar (total: 54.4s)

sample81.0ms

Algorithm
intervals
Results
69.0ms315×body80valid

simplify455.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
455.0ms
(* (* (/ 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: 12.2b

localize39.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (/ PI (- (* b b) (* a a))) a)
4.1b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
3.4b
(- (* b b) (* a a))
3.4b
(- (* b b) (* a a))

rewrite57.0ms

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)
13.0ms
(- (* 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))

series325.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(/ (/ PI (- (* b b) (* a a))) a)
100.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
55.0ms
(- (* b b) (* a a))
40.0ms
(- (* b b) (* a a))

simplify20.9s

Counts
152 → 152
Calls
152 calls:
Slowest
614.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
570.0ms
(/ (/ (sqrt PI) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a))))) (sqrt a))
456.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
366.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a))))) (* (cbrt a) (cbrt a)))
361.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a))))) (sqrt a))

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize55.0ms

Local error

Found 4 expressions with local error:

4.1b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
3.4b
(- (* b b) (* a a))
0.6b
(/ PI (- (* b b) (* a a)))
0.3b
(/ PI (- b a))

rewrite27.0ms

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
10.0ms
(/ 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)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
80.0ms
(/ PI (- b a))
77.0ms
(/ PI (- (* b b) (* a a)))
58.0ms
(- (* b b) (* a a))

simplify4.3s

Counts
92 → 117
Calls
92 calls:
Slowest
257.0ms
(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
230.0ms
(/ (exp (* b b)) (exp (* a a)))
205.0ms
(- (log PI) (log (- (* b b) (* a a))))
174.0ms
(/ 1 (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))
173.0ms
(/ PI (sqrt (- (* b b) (* a a))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

localize50.0ms

Local error

Found 4 expressions with local error:

4.1b
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
0.3b
(/ PI (- b a))
0.3b
(/ PI (- b a))
0.2b
(* (/ 1 (+ b a)) (/ PI (- b a)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
71×*-un-lft-identity
64×times-frac
41×add-cube-cbrt
30×add-exp-log
21×associate-*r*
20×add-cbrt-cube
18×associate-*l*
11×distribute-lft-out-- difference-of-squares
10×associate-/r* div-exp
8×prod-exp associate-/r/
6×pow1 cbrt-undiv associate-/l* unswap-sqr
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
3×flip3-- flip-- distribute-lft-out
2×rec-exp clear-num frac-2neg 1-exp
1×frac-times flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+ fma-udef
Counts
4 → 163
Calls
4 calls:
Slowest
30.0ms
(* (/ 1 (+ b a)) (/ PI (- b 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)) (/ (/ PI (- b a)) a)))

series364.0ms

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)))
94.0ms
(* (/ 1 (+ b a)) (/ PI (- b a)))
64.0ms
(/ PI (- b a))
63.0ms
(/ PI (- b a))

simplify6.6s

Counts
160 → 175
Calls
160 calls:
Slowest
551.0ms
(* (* (* (/ 1 (+ b a)) (/ 1 (+ b a))) (/ 1 (+ b a))) (* (* (/ PI (- b a)) (/ PI (- b a))) (/ PI (- b a))))
368.0ms
(* (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a))))
232.0ms
(* (/ (* (* 1 1) 1) (* (* (+ b a) (+ b a)) (+ b a))) (* (* (/ PI (- b a)) (/ PI (- b a))) (/ PI (- b a))))
228.0ms
(* (/ 1 (+ b a)) (/ PI (- b a)))
218.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize76.0ms

Local error

Found 4 expressions with local error:

4.1b
(fma (* (/ 1 (+ b a)) (/ 1 (/ (- b a) PI))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
0.3b
(/ PI (- b a))
0.3b
(/ 1 (/ (- b a) PI))
0.3b
(/ (- b a) PI)

rewrite50.0ms

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
16.0ms
(/ PI (- b a))
15.0ms
(/ (- b a) PI)
15.0ms
(/ 1 (/ (- b a) PI))
1.0ms
(fma (* (/ 1 (+ b a)) (/ 1 (/ (- b a) PI))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))

series746.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
529.0ms
(fma (* (/ 1 (+ b a)) (/ 1 (/ (- b a) PI))) (/ -1 b) (* (/ 1 (+ b a)) (/ (/ PI (- b a)) a)))
86.0ms
(/ 1 (/ (- b a) PI))
71.0ms
(/ (- b a) PI)
60.0ms
(/ PI (- b a))

simplify9.4s

Counts
235 → 207
Calls
235 calls:
Slowest
338.0ms
(/ (* (* 1 1) 1) (/ (* (* (- b a) (- b a)) (- b a)) (* (* PI PI) PI)))
325.0ms
(/ (* (cbrt 1) (cbrt 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)))
284.0ms
(/ (sqrt 1) (/ (* (cbrt (- b a)) (cbrt (- b a))) (* (cbrt PI) (cbrt PI))))
216.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

regimes332.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.8s9630×body80valid