Details

Time bar (total: 2.2m)

sample83.0ms

Algorithm
intervals
Results
32.0ms194×body80valid
15.0ms30×body1280valid
11.0ms256×pre80true
5.0ms14×body640valid
5.0ms16×body320valid
0.0ms2×body160valid

simplify159.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
159.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize22.0ms

Local error

Found 2 expressions with local error:

0.8b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite228.0ms

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
192.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
34.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series129.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
70.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
59.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify4.7s

Counts
104 → 108
Calls
104 calls:
Slowest
249.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
243.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
240.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
237.0ms
(/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)))
230.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))

prune988.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))

rewrite661.0ms

Algorithm
rewrite-expression-head
Rules
512×*-un-lft-identity
328×add-sqr-sqrt
263×times-frac
252×prod-diff
213×add-cube-cbrt
150×distribute-lft-out
65×associate--r+
46×difference-of-squares
42×fma-neg
32×associate-/r/
25×distribute-lft-out--
16×flip3-+ flip-+ div-inv
11×add-log-exp
10×associate-/r*
8×add-cbrt-cube add-exp-log
6×associate-/l*
4×expm1-log1p-u pow1 diff-log insert-posit16 log1p-expm1-u
3×sub-neg flip3-- flip--
2×cbrt-undiv clear-num frac-2neg div-exp frac-sub
1×associate--r-
Counts
4 → 417
Calls
4 calls:
Slowest
400.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
190.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
32.0ms
(/ beta (+ (+ alpha beta) 2.0))
21.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series347.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
100.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
71.0ms
(/ beta (+ (+ alpha beta) 2.0))
55.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify1.2m

Counts
593 → 429
Calls
593 calls:
Slowest
733.0ms
(fma (/ 1 (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ beta (cbrt (+ (+ alpha beta) 2.0))) (- (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 1)))
554.0ms
(fma (- (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
510.0ms
(fma (/ (sqrt beta) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (sqrt beta) (cbrt (+ (+ alpha beta) 2.0))) (- (* (- (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)))))
459.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) (sqrt (+ (+ alpha beta) 2.0))) (/ (cbrt beta) (sqrt (+ (+ alpha beta) 2.0))) (- (* (- (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)))))
457.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) 1) (/ (cbrt beta) (+ (+ alpha beta) 2.0)) (- (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))

prune4.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.1b
(* beta (/ 1 (+ (+ alpha beta) 2.0)))
0.0b
(/ 1 (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
209×*-un-lft-identity
108×times-frac
103×add-sqr-sqrt
91×add-cube-cbrt
69×distribute-lft-out
63×prod-diff
21×fma-neg associate-*r*
19×add-exp-log
14×associate-/r/
13×add-cbrt-cube
10×associate-/r*
7×pow1 flip3-+ flip-+ div-inv
6×associate-/l* add-log-exp
5×div-exp
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-*l* unswap-sqr
2×rec-exp clear-num frac-2neg 1-exp cbrt-unprod difference-of-squares
1×sub-neg flip3-- diff-log pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip flip-- distribute-lft-out-- inv-pow
Counts
4 → 233
Calls
4 calls:
Slowest
177.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
50.0ms
(* beta (/ 1 (+ (+ alpha beta) 2.0)))
46.0ms
(/ 1 (+ (+ alpha beta) 2.0))
45.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series298.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
71.0ms
(* beta (/ 1 (+ (+ alpha beta) 2.0)))
66.0ms
(/ alpha (+ (+ alpha beta) 2.0))
45.0ms
(/ 1 (+ (+ alpha beta) 2.0))

simplify18.3s

Counts
285 → 245
Calls
285 calls:
Slowest
517.0ms
(* (* (* beta beta) beta) (* (* (/ 1 (+ (+ alpha beta) 2.0)) (/ 1 (+ (+ alpha beta) 2.0))) (/ 1 (+ (+ alpha beta) 2.0))))
444.0ms
(fma (- (cbrt 1.0)) (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0))))
357.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
331.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
324.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

localize54.0ms

Local error

Found 4 expressions with local error:

7.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
0.8b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
195×*-un-lft-identity
106×times-frac
93×add-sqr-sqrt
88×add-cube-cbrt
63×cbrt-prod prod-diff distribute-lft-out
21×fma-neg
14×associate-/r/
7×flip3-+ flip-+ div-inv
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cbrt-div pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 201
Calls
4 calls:
Slowest
216.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
21.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
21.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
20.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series690.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
200.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
172.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
103.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify15.9s

Counts
229 → 213
Calls
229 calls:
Slowest
327.0ms
(- (exp (* 1/3 (+ (log beta) (log 0.5)))) (+ (* 0.16666666666666666 (* beta (exp (* 1/3 (+ (log beta) (log 0.5)))))) (* 0.16666666666666666 (* (exp (* 1/3 (+ (log beta) (log 0.5)))) alpha))))
311.0ms
(- (exp (* 1/3 (+ (log beta) (log 0.5)))) (+ (* 0.16666666666666666 (* beta (exp (* 1/3 (+ (log beta) (log 0.5)))))) (* 0.16666666666666666 (* (exp (* 1/3 (+ (log beta) (log 0.5)))) alpha))))
284.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
280.0ms
(- (exp (* 1/3 (+ (log beta) (log 0.5)))) (+ (* 0.16666666666666666 (* beta (exp (* 1/3 (+ (log beta) (log 0.5)))))) (* 0.16666666666666666 (* (exp (* 1/3 (+ (log beta) (log 0.5)))) alpha))))
279.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))

prune2.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

regimes199.0ms

Accuracy

75.8% (3.1b remaining)

Error of 5.9b against oracle of 2.8b and baseline of 15.7b

bsearch82.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
626.0ms5853×body80valid
436.0ms848×body1280valid
315.0ms675×body640valid
303.0ms8000×pre80true
99.0ms387×body320valid
39.0ms237×body160valid