Details

Time bar (total: 46.3s)

sample70.0ms

Algorithm
intervals
Results
45.0ms256×body80valid
9.0ms256×pre80true

simplify1.3s

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize42.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
0.0b
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(+ (+ 2 (+ beta alpha)) 1.0)

rewrite670.0ms

Algorithm
rewrite-expression-head
Rules
5713×*-un-lft-identity
3256×times-frac
2994×distribute-lft-out
886×add-sqr-sqrt add-cube-cbrt
197×associate-/l*
102×associate-/r/
53×flip3-+ flip-+
51×div-inv
20×add-cbrt-cube add-exp-log
16×associate-/r*
13×add-log-exp
10×cbrt-undiv div-exp
6×sum-log
5×fma-def
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Counts
4 → 1445
Calls
4 calls:
Slowest
261.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
128.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
109.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
73.0ms
(+ (+ 2 (+ beta alpha)) 1.0)

series578.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
232.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
211.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
110.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
25.0ms
(+ (+ 2 (+ beta alpha)) 1.0)

simplify1.2s

Counts
1457 → 1457

prune16.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.9b

localize98.0ms

Local error

Found 4 expressions with local error:

4.1b
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
4.1b
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
4.1b
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
2.0b
(/ (/ (* (cbrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))) 1) (sqrt (+ 2 (+ beta alpha))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
83×times-frac
41×add-sqr-sqrt add-cube-cbrt
40×sqrt-prod
33×distribute-lft-out
18×add-exp-log
15×cbrt-prod
11×add-cbrt-cube
10×div-inv
9×div-exp
8×associate-/r*
7×associate-/l*
6×cbrt-div
5×cbrt-undiv
4×expm1-log1p-u pow1 flip3-+ flip-+ insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×sqrt-div 1-exp prod-exp associate-/r/
1×clear-num frac-2neg cbrt-unprod associate-/l/
Counts
4 → 149
Calls
4 calls:
Slowest
58.0ms
(/ (/ (* (cbrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))) 1) (sqrt (+ 2 (+ beta alpha))))
17.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
16.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
8.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))

series602.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
324.0ms
(/ (/ (* (cbrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))) 1) (sqrt (+ 2 (+ beta alpha))))
97.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
93.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
87.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))

simplify1.4s

Counts
161 → 161

prune2.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.9b

localize114.0ms

Local error

Found 4 expressions with local error:

4.1b
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
4.1b
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
3.8b
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
3.8b
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
14×add-sqr-sqrt
12×distribute-lft-out
10×cbrt-prod sqrt-prod
8×add-cube-cbrt
6×pow1
4×expm1-log1p-u cbrt-div flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 hypot-def
Counts
4 → 78
Calls
4 calls:
Slowest
36.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
34.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
24.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
16.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))

series364.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
94.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
80.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
66.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))

simplify864.0ms

Counts
90 → 90

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.9b

localize39.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
0.7b
(fma (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))) 1.0)
0.1b
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (fma (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))) 1.0))
0.0b
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite491.0ms

Algorithm
rewrite-expression-head
Rules
2764×*-un-lft-identity
1933×times-frac
1284×distribute-lft-out
624×add-sqr-sqrt add-cube-cbrt
197×associate-/l*
64×associate-/r/
33×flip3-+ flip-+ div-inv
20×add-cbrt-cube add-exp-log
13×associate-/r*
10×cbrt-undiv div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×clear-num frac-2neg
1×fma-udef
Counts
4 → 943
Calls
4 calls:
Slowest
194.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (fma (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))) 1.0))
125.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
110.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0ms
(fma (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))) 1.0)

series863.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
428.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (fma (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))) 1.0))
175.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
141.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
118.0ms
(fma (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))) 1.0)

simplify1.4s

Counts
955 → 955

prune12.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 1.9b

regimes171.0ms

Accuracy

42.8% (1.5b remaining)

Error of 2.8b against oracle of 1.3b and baseline of 4.0b

bsearch131.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.7s8000×body80valid
278.0ms8000×pre80true