Details

Time bar (total: 2.5m)

sample79.0ms

Algorithm
intervals
Results
19.0ms184×body80valid
12.0ms256×pre80true
11.0ms26×body640valid
11.0ms21×body1280valid
6.0ms18×body320valid
1.0ms7×body160valid

simplify151.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
151.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite183.0ms

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
139.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
41.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series190.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
108.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
82.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify5.0s

Counts
104 → 108
Calls
104 calls:
Slowest
576.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
278.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
245.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
238.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
223.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.9b

localize28.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ 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))

rewrite718.0ms

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
439.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
203.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
40.0ms
(/ alpha (+ (+ alpha beta) 2.0))
25.0ms
(/ beta (+ (+ alpha beta) 2.0))

series334.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
86.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
64.0ms
(/ beta (+ (+ alpha beta) 2.0))
64.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify1.2m

Counts
593 → 429
Calls
593 calls:
Slowest
522.0ms
(fma (- (sqrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (sqrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (sqrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (sqrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
492.0ms
(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))))))
491.0ms
(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))))))
464.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (cbrt beta) (cbrt (+ (+ 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))))))
464.0ms
(fma (- (sqrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (sqrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (sqrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (sqrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))

prune4.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize87.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
141×*-un-lft-identity
69×add-sqr-sqrt
64×add-cube-cbrt
63×prod-diff
61×times-frac
45×distribute-lft-out
21×fma-neg
15×cbrt-prod
8×associate-/r/
7×flip3-+ flip-+
6×cbrt-div add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log 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 → 156
Calls
4 calls:
Slowest
180.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
20.0ms
(cbrt (+ (+ alpha beta) 2.0))
11.0ms
(cbrt (+ (+ alpha beta) 2.0))
11.0ms
(cbrt (+ (+ alpha beta) 2.0))

series493.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(cbrt (+ (+ alpha beta) 2.0))
134.0ms
(cbrt (+ (+ alpha beta) 2.0))
132.0ms
(cbrt (+ (+ alpha beta) 2.0))
89.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify15.3s

Counts
184 → 168
Calls
184 calls:
Slowest
599.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
317.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
313.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
289.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
280.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize85.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(cbrt (+ (+ alpha beta) 2.0))

rewrite598.0ms

Algorithm
rewrite-expression-head
Rules
367×*-un-lft-identity
191×add-sqr-sqrt
189×prod-diff
183×times-frac
176×add-cube-cbrt
111×distribute-lft-out
63×fma-neg
24×associate-/r/
13×flip3-+ flip-+
12×div-inv
10×add-log-exp
6×difference-of-squares
5×cbrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×sub-neg flip3-- diff-log flip-- distribute-lft-out--
2×cbrt-div
1×pow1/3
Counts
4 → 324
Calls
4 calls:
Slowest
220.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
175.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
172.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
21.0ms
(cbrt (+ (+ alpha beta) 2.0))

series467.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(cbrt (+ (+ alpha beta) 2.0))
120.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
111.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
108.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify35.6s

Counts
472 → 336
Calls
472 calls:
Slowest
572.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
344.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
328.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))
320.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
316.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))

prune5.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

regimes176.0ms

Accuracy

76.3% (3.1b remaining)

Error of 6.0b against oracle of 2.9b and baseline of 16.0b

bsearch98.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
598.0ms5907×body80valid
392.0ms792×body1280valid
336.0ms727×body640valid
332.0ms8000×pre80true
129.0ms388×body320valid
33.0ms186×body160valid