Details

Time bar (total: 19.5s)

sample84.0ms

Algorithm
intervals
Results
21.0ms191×body80valid
18.0ms33×body1280valid
18.0ms256×pre80true
7.0ms16×body640valid
3.0ms11×body320valid
1.0ms5×body160valid

simplify493.0ms

Counts
1 → 1
Iterations
IterNodes
15445
14445
13442
12437
11416
10364
9276
8211
7186
6152
5112
469
350
233
120
010

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.3b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite206.0ms

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:
40.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
164.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series177.0ms

Counts
2 → 6
Calls
2 calls:
84.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
93.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts
108 → 108
Iterations
IterNodes
33331
21010
1340
0130

prune980.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.6b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
1.3b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite240.0ms

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:
35.0ms
(/ beta (+ (+ alpha beta) 2.0))
32.0ms
(/ alpha (+ (+ alpha beta) 2.0))
166.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series242.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(/ beta (+ (+ alpha beta) 2.0))
61.0ms
(/ alpha (+ (+ alpha beta) 2.0))
110.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.6s

Counts
191 → 191
Iterations
IterNodes
33788
21183
1490
0224

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt beta)
0.6b
(cbrt beta)
0.6b
(cbrt beta)
1.3b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite225.0ms

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:
1.0ms
(cbrt beta)
1.0ms
(cbrt beta)
2.0ms
(cbrt beta)
215.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series993.0ms

Counts
4 → 12
Calls
4 calls:
322.0ms
(cbrt beta)
285.0ms
(cbrt beta)
261.0ms
(cbrt beta)
126.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts
156 → 156
Iterations
IterNodes
32823
2919
1387
0179

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (+ alpha beta) 3)
0.0b
(* (+ alpha beta) (+ alpha beta))
3.6b
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
24.9b
(fma (/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3))) (+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0))) 1.0)

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
209×*-un-lft-identity
86×distribute-lft-out
65×times-frac
61×add-sqr-sqrt
52×unpow-prod-down cube-prod
31×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
13×associate-/r*
12×pow1
9×add-cbrt-cube add-exp-log
8×flip3-+ flip-+
6×swap-sqr sum-cubes
5×associate-/l*
4×expm1-log1p-u frac-times associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow
2×cube-div associate-*l/ associate-*r/ associate-/r/ associate-/l/
1×pow2 distribute-rgt-in cube-mult pow-to-exp cbrt-undiv clear-num pow-pow frac-2neg distribute-lft-in pow-plus flip3-- unpow3 div-sub div-exp pow-prod-down pow-exp prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef div-inv flip-- rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 187
Calls
4 calls:
13.0ms
(pow (+ alpha beta) 3)
49.0ms
(* (+ alpha beta) (+ alpha beta))
68.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
1.0ms
(fma (/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3))) (+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0))) 1.0)

series378.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(pow (+ alpha beta) 3)
31.0ms
(* (+ alpha beta) (+ alpha beta))
133.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
157.0ms
(fma (/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3))) (+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0))) 1.0)

simplify1.5s

Counts
199 → 199
Iterations
IterNodes
22381
1657
0235

prune2.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

regimes224.0ms

Accuracy

54.1% (11.7b remaining)

Error of 14.6b against oracle of 2.9b and baseline of 28.4b

bsearch126.0ms

Steps
ItersRangePoint
9
9.825007618840887
8287404.793038737
429068.6689692988

simplify15.0ms

Iterations
IterNodes
240
140
034

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.1s5842×body80valid
417.0ms895×body1280valid
333.0ms8000×pre80true
249.0ms708×body640valid
119.0ms370×body320valid
30.0ms185×body160valid