Details

Time bar (total: 50.0s)

sample52.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
8.0ms256×pre80true

simplify1.7s

Counts
1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize50.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (+ 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)

rewrite664.0ms

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
230.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
126.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
98.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
92.0ms
(+ (+ 2 (+ beta alpha)) 1.0)

series616.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
259.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
207.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
131.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
18.0ms
(+ (+ 2 (+ beta alpha)) 1.0)

simplify1.4s

Counts
1457 → 1457

prune16.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.9b

localize62.0ms

Local error

Found 4 expressions with local error:

9.2b
(* (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
1.9b
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
1.9b
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
0.2b
(/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha)))

rewrite323.0ms

Algorithm
rewrite-expression-head
Rules
816×*-un-lft-identity
480×times-frac
387×distribute-lft-out
236×associate-*r*
203×add-sqr-sqrt
176×sqrt-prod
171×add-cube-cbrt
15×add-cbrt-cube add-exp-log
14×associate-/r/
12×flip3-+ flip-+
10×sqrt-div
8×pow1 associate-*l* associate-/l* unswap-sqr
7×div-inv
5×associate-/r*
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×prod-exp cbrt-unprod
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ hypot-def associate-/l/
1×clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
4 → 389
Calls
4 calls:
Slowest
221.0ms
(* (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
45.0ms
(/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha)))
17.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
17.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))

series685.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
310.0ms
(/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha)))
216.0ms
(* (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
86.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
73.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))

simplify1.3s

Counts
401 → 401

prune5.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.9b

localize79.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (sqrt (* (cbrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (cbrt (+ 1.0 (+ beta (fma beta alpha alpha)))))) (* (sqrt (cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))) (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
3.6b
(* (sqrt (cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))) (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
2.2b
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
2.2b
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))

rewrite559.0ms

Algorithm
rewrite-expression-head
Rules
722×*-un-lft-identity
445×times-frac
342×distribute-lft-out
237×associate-*r*
191×add-sqr-sqrt
152×add-cube-cbrt
145×sqrt-prod
116×cbrt-div
88×sqrt-div
84×frac-times
64×flip3-+ flip-+
40×associate-*l/
27×add-cbrt-cube associate-*r/ add-exp-log
19×cbrt-prod
15×associate-*l*
12×associate-/r/ unswap-sqr
11×pow1
10×prod-exp cbrt-unprod
6×cbrt-undiv div-exp div-inv
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
2×pow1/3 *-commutative
Counts
4 → 397
Calls
4 calls:
Slowest
322.0ms
(* (sqrt (* (cbrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (cbrt (+ 1.0 (+ beta (fma beta alpha alpha)))))) (* (sqrt (cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))) (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
206.0ms
(* (sqrt (cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))) (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
8.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
7.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
610.0ms
(* (sqrt (* (cbrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (cbrt (+ 1.0 (+ beta (fma beta alpha alpha)))))) (* (sqrt (cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))) (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
490.0ms
(* (sqrt (cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))) (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
99.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))
82.0ms
(cbrt (+ 1.0 (+ beta (fma beta alpha alpha))))

simplify1.8s

Counts
409 → 409

prune6.9s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.9b

localize46.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
1.6b
(* (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) 1) (/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0)))
0.1b
(/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
0.0b
(/ 1 (+ 2 (+ beta alpha)))

rewrite691.0ms

Algorithm
rewrite-expression-head
Rules
1077×*-un-lft-identity
704×times-frac
513×distribute-lft-out
328×add-sqr-sqrt
252×add-cube-cbrt
132×associate-*r*
114×add-exp-log
97×associate-*l*
69×div-exp
49×add-cbrt-cube
40×associate-/r/
29×associate-/l*
25×prod-exp
23×cbrt-undiv
21×flip3-+ flip-+ div-inv
20×unswap-sqr
17×1-exp
16×associate-/r*
9×cbrt-unprod
7×pow1 rec-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-/l/
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative pow-flip inv-pow
Counts
4 → 571
Calls
4 calls:
Slowest
358.0ms
(* (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) 1) (/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0)))
157.0ms
(/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
115.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
36.0ms
(/ 1 (+ 2 (+ beta alpha)))

series505.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(* (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) 1) (/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0)))
129.0ms
(/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
123.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
55.0ms
(/ 1 (+ 2 (+ beta alpha)))

simplify1.0s

Counts
583 → 583

prune6.1s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.9b

regimes169.0ms

Accuracy

0% (2.2b remaining)

Error of 3.3b against oracle of 1.1b and baseline of 3.3b

bsearch2.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s8000×body80valid
327.0ms8000×pre80true