Details

Time bar (total: 2.3m)

sample83.0ms

Algorithm
intervals
Results
26.0ms29×body1280valid
18.0ms190×body80valid
12.0ms256×pre80true
6.0ms15×body640valid
5.0ms17×body320valid
1.0ms5×body160valid

simplify156.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
156.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize18.0ms

Local error

Found 2 expressions with local error:

1.9b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
104×*-un-lft-identity
50×times-frac
47×add-sqr-sqrt
34×distribute-lft-out
31×fma-def
25×add-cube-cbrt
11×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-cbrt-cube add-exp-log associate-/r/ add-log-exp
3×flip3-+ flip-+
2×expm1-log1p-u pow1 div-sub insert-posit16 log1p-expm1-u div-inv associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- flip--
Counts
2 → 102
Calls
2 calls:
Slowest
177.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
51.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series173.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
90.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
82.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify4.8s

Counts
104 → 108
Calls
104 calls:
Slowest
249.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
244.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
243.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
234.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
231.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))

prune996.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.7b

localize38.0ms

Local error

Found 3 expressions with local error:

1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
182×*-un-lft-identity
91×times-frac
85×add-sqr-sqrt
80×add-cube-cbrt
63×prod-diff
60×distribute-lft-out
21×fma-neg
12×associate-/r/
10×associate-/r*
7×add-cbrt-cube add-exp-log
6×flip3-+ flip-+ div-inv associate-/l*
5×add-log-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 182
Calls
3 calls:
Slowest
206.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
45.0ms
(/ beta (+ (+ alpha beta) 2.0))
24.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series234.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
98.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
70.0ms
(/ beta (+ (+ alpha beta) 2.0))
66.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify15.6s

Counts
242 → 191
Calls
242 calls:
Slowest
361.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
355.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))
350.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
338.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
322.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.5b

localize40.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.6b
(cbrt beta)
0.6b
(cbrt beta)
0.6b
(cbrt beta)

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
126×*-un-lft-identity
69×add-sqr-sqrt
64×add-cube-cbrt
63×prod-diff
61×times-frac
36×distribute-lft-out
21×fma-neg
9×cbrt-prod
8×associate-/r/
6×add-log-exp
4×expm1-log1p-u pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 log1p-expm1-u div-inv
3×pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 144
Calls
4 calls:
Slowest
189.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.0ms
(cbrt beta)
1.0ms
(cbrt beta)
1.0ms
(cbrt beta)

series911.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
273.0ms
(cbrt beta)
271.0ms
(cbrt beta)
260.0ms
(cbrt beta)
106.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify12.1s

Counts
172 → 156
Calls
172 calls:
Slowest
358.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))
357.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))
286.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
279.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))
278.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.5b

localize32.0ms

Local error

Found 4 expressions with local error:

10.6b
(+ (/ (/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)
0.5b
(/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0)))
0.2b
(/ (/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
0.0b
(sqrt (+ (+ alpha beta) 2.0))

rewrite648.0ms

Algorithm
rewrite-expression-head
Rules
1753×*-un-lft-identity
1456×times-frac
925×sqrt-prod
829×add-sqr-sqrt
556×distribute-lft-out
536×add-cube-cbrt
374×fma-def
145×distribute-lft-out-- difference-of-squares
51×associate-/l*
42×sqrt-div
40×associate-/r/
22×flip3-+ flip-+
20×div-inv
16×associate-/r*
11×add-cbrt-cube add-exp-log
6×add-log-exp
5×pow1 div-sub
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×associate-/l/
2×clear-num frac-2neg
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-- pow1/2 associate-+l- hypot-def flip--
Counts
4 → 927
Calls
4 calls:
Slowest
363.0ms
(+ (/ (/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)
132.0ms
(/ (/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
47.0ms
(sqrt (+ (+ alpha beta) 2.0))
44.0ms
(/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0)))
93.0ms
(+ (/ (/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)
68.0ms
(/ (/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
59.0ms
(sqrt (+ (+ alpha beta) 2.0))

simplify1.4m

Counts
1293 → 939
Calls
1293 calls:
Slowest
527.0ms
(/ (- beta alpha) (sqrt (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
516.0ms
(/ (- (sqrt beta) (sqrt alpha)) (sqrt (+ (+ alpha beta) 2.0)))
420.0ms
(- (* (sqrt 0.5) beta) (+ (* 1/2 (* (pow beta 2) (sqrt 0.125))) (* (sqrt 0.5) alpha)))
334.0ms
(/ (sqrt (+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))) (sqrt (+ (+ alpha beta) 2.0)))
334.0ms
(/ (sqrt (+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))) (sqrt (+ (+ alpha beta) 2.0)))

prune10.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.5b

regimes133.0ms

Accuracy

73.4% (3.5b remaining)

Error of 6.4b against oracle of 2.9b and baseline of 16.0b

bsearch281.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
578.0ms811×body1280valid
572.0ms5893×body80valid
307.0ms712×body640valid
290.0ms8000×pre80true
100.0ms371×body320valid
39.0ms213×body160valid