Details

Time bar (total: 16.8s)

sample104.0ms

Algorithm
intervals
Results
42.0ms208×body80valid
12.0ms256×pre80true
11.0ms16×body1280valid
10.0ms18×body640valid
4.0ms9×body320valid
2.0ms5×body160valid

simplify816.0ms

Counts
1 → 1

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.1b

localize35.0ms

Local error

Found 3 expressions with local error:

1.4b
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.0b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
0.0b
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
31×add-sqr-sqrt times-frac
23×add-cube-cbrt
10×distribute-lft-out
9×associate-/l*
7×associate-/r* add-cbrt-cube add-exp-log
4×distribute-lft-out-- difference-of-squares associate-/l/
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+ div-inv
1×flip3-- div-sub fma-udef flip--
Counts
3 → 95
Calls
3 calls:
Slowest
32.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
31.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
1.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series374.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
188.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
100.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
86.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

simplify528.0ms

Counts
138 → 104

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.9b

localize37.0ms

Local error

Found 4 expressions with local error:

2.4b
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.2b
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
0.0b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
0.0b
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
47×add-sqr-sqrt
41×times-frac
32×add-cube-cbrt
19×add-exp-log
18×associate-*r*
13×add-cbrt-cube
8×distribute-lft-out associate-/l*
7×pow1 associate-/r*
5×div-exp
4×expm1-log1p-u flip3-+ associate-*l* prod-exp associate-/r/ flip-+ insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×cbrt-undiv div-inv unswap-sqr
2×frac-times rec-exp clear-num frac-2neg 1-exp associate-*l/ cbrt-unprod associate-/l/
1×flip3-- div-sub pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef pow-flip flip-- inv-pow
Counts
4 → 141
Calls
4 calls:
Slowest
34.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
25.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
14.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))
1.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series545.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
212.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
123.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))
120.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
91.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))

simplify669.0ms

Counts
185 → 153

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.9b

localize63.0ms

Local error

Found 4 expressions with local error:

3.5b
(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
1.4b
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.1b
(exp (log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
0.0b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt *-un-lft-identity
17×add-cube-cbrt
15×times-frac
7×add-exp-log
6×pow1 log-prod add-cbrt-cube
5×associate-/l*
4×expm1-log1p-u exp-prod insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×associate-/r* exp-sum
2×log-pow associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp rem-log-exp fma-udef div-inv flip-- rem-exp-log
Counts
4 → 85
Calls
4 calls:
Slowest
15.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
6.0ms
(exp (log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
3.0ms
(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
0.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series878.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
338.0ms
(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
222.0ms
(exp (log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
207.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
111.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

simplify326.0ms

Counts
118 → 97

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.9b

localize75.0ms

Local error

Found 4 expressions with local error:

6.7b
(fma (* (* (+ beta alpha) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.3b
(* (* (+ beta alpha) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))))
0.3b
(* (+ beta alpha) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))))
0.1b
(sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
57×sqrt-prod
53×*-un-lft-identity
44×add-sqr-sqrt
42×associate-*r*
40×times-frac
31×add-cube-cbrt
16×sqrt-div
13×pow1
11×frac-times add-cbrt-cube associate-*l/ add-exp-log
10×distribute-lft-out
9×flip3-+ flip-+
6×associate-/r/
5×associate-*l*
4×expm1-log1p-u pow-prod-down prod-exp associate-*r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×rem-sqrt-square sqrt-pow1 div-inv
2×*-commutative
1×pow1/2 fma-udef pow-flip inv-pow
Counts
4 → 145
Calls
4 calls:
Slowest
107.0ms
(* (* (+ beta alpha) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))))
34.0ms
(* (+ beta alpha) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))))
12.0ms
(sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
1.0ms
(fma (* (* (+ beta alpha) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series671.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
209.0ms
(fma (* (* (+ beta alpha) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
189.0ms
(sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
177.0ms
(* (+ beta alpha) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))))
96.0ms
(* (* (+ beta alpha) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))) (sqrt (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))))

simplify430.0ms

Counts
181 → 157

prune2.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.9b

regimes315.0ms

Accuracy

0% (0.3b remaining)

Error of 11.9b against oracle of 11.6b and baseline of 11.9b

bsearch5.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.3s6419×body80valid
412.0ms571×body640valid
399.0ms506×body1280valid
372.0ms8000×pre80true
174.0ms329×body320valid
48.0ms175×body160valid