Details

Time bar (total: 22.9s)

sample107.0ms

Algorithm
intervals
Results
33.0ms214×body80valid
25.0ms15×body1280valid
13.0ms256×pre80true
10.0ms15×body640valid
3.0ms7×body320valid
2.0ms5×body160valid

simplify718.0ms

Counts
1 → 1

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.1b

localize22.0ms

Local error

Found 3 expressions with local error:

1.5b
(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))))

rewrite59.0ms

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
40.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
16.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
0.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series415.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
209.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
109.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
97.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

simplify1.3s

Counts
104 → 104

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.8b

localize58.0ms

Local error

Found 4 expressions with local error:

2.9b
(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))))

rewrite60.0ms

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
35.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
12.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
10.0ms
(/ 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)

series487.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
117.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
88.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))
86.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

simplify643.0ms

Counts
153 → 153

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.8b

localize56.0ms

Local error

Found 4 expressions with local error:

2.9b
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha)))) 1.0)
0.2b
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
0.0b
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))
0.0b
(- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
238×*-un-lft-identity
232×add-sqr-sqrt
213×add-cube-cbrt
169×prod-diff
31×div-inv
18×associate-*r*
17×add-exp-log
13×fma-neg
11×add-cbrt-cube
8×distribute-lft-out
7×pow1
6×add-log-exp
4×expm1-log1p-u associate-/r* flip3-+ div-exp associate-*l* prod-exp associate-/r/ flip-+ insert-posit16 log1p-expm1-u distribute-lft-out-- difference-of-squares
3×associate-/l* unswap-sqr
2×frac-times cbrt-undiv rec-exp 1-exp associate-*l/ cbrt-unprod
1×clear-num sub-neg frac-2neg flip3-- distribute-rgt-out-- diff-log pow-prod-down associate-*r/ un-div-inv *-commutative frac-sub fma-udef pow-flip flip-- inv-pow sub-div
Counts
4 → 308
Calls
4 calls:
Slowest
59.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
14.0ms
(- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha))))
8.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))
0.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha)))) 1.0)

series605.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
266.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha)))) 1.0)
132.0ms
(- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha))))
130.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
78.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))

simplify1.4s

Counts
320 → 320

prune5.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.8b

localize42.0ms

Local error

Found 4 expressions with local error:

2.9b
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (log1p (expm1 (- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha)))))) 1.0)
0.3b
(expm1 (- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha)))))
0.2b
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
0.0b
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
29×add-sqr-sqrt
26×times-frac
22×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
8×distribute-lft-out
7×pow1
5×log1p-expm1-u
4×expm1-log1p-u associate-/r* flip3-+ div-exp associate-*l* prod-exp associate-/r/ flip-+ insert-posit16 add-log-exp
3×associate-/l* unswap-sqr
2×frac-times cbrt-undiv rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×expm1-log1p clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef pow-flip inv-pow expm1-udef
Counts
4 → 112
Calls
4 calls:
Slowest
58.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
15.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))
1.0ms
(expm1 (- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha)))))
1.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (log1p (expm1 (- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha)))))) 1.0)

series700.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
283.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (log1p (expm1 (- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha)))))) 1.0)
211.0ms
(expm1 (- (/ beta (fma 2 i (+ beta alpha))) (/ alpha (fma 2 i (+ beta alpha)))))
105.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
100.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))

simplify2.3s

Counts
124 → 124

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.8b

regimes293.0ms

Accuracy

0% (0.3b remaining)

Error of 12.2b against oracle of 11.9b and baseline of 12.2b

bsearch3.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
952.0ms6379×body80valid
775.0ms8000×pre80true
418.0ms512×body1280valid
416.0ms555×body640valid
177.0ms357×body320valid
54.0ms197×body160valid