Details

Time bar (total: 22.8s)

sample54.0ms

Algorithm
intervals
Results
14.0ms213×body80valid
6.0ms256×pre80true
4.0ms16×body640valid
4.0ms12×body1280valid
2.0ms10×body320valid
1.0ms5×body160valid

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 3 (105.0ms)

IterNodesCost
01529
13129
210627
347726
4227026
done500126

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
0.0b
(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
1.7b
(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
33×add-sqr-sqrt
32×times-frac
23×add-cube-cbrt
10×distribute-lft-out
9×associate-/l*
7×add-exp-log associate-/r* add-cbrt-cube
5×distribute-lft-out-- difference-of-squares
4×associate-/l/
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+ div-inv
1×flip3-- div-sub flip-- fma-udef
Counts
3 → 93
Calls
3 calls:
36.0ms
(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
29.0ms
(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0ms
(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series451.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
139.0ms
(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
233.0ms
(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify2.2s

Counts
102 → 102
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01721935
13911877
210951746
335391744
done50001741

prune427.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0b
(/ 1 (fma 2.0 i (+ alpha beta)))
0.2b
(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
3.6b
(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
48×add-sqr-sqrt
40×times-frac
31×add-cube-cbrt
19×add-exp-log
13×associate-*r* add-cbrt-cube
8×associate-/l*
7×pow1 associate-/r* distribute-lft-out
5×div-exp distribute-lft-out-- difference-of-squares
4×expm1-log1p-u associate-*l* prod-exp log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ flip-+ div-inv unswap-sqr
2×frac-times rec-exp frac-2neg 1-exp associate-*l/ clear-num associate-/r/ cbrt-unprod associate-/l/
1×flip3-- pow-flip div-sub associate-*r/ pow-prod-down un-div-inv *-commutative flip-- fma-udef inv-pow
Counts
4 → 134
Calls
4 calls:
49.0ms
(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
5.0ms
(/ 1 (fma 2.0 i (+ alpha beta)))
33.0ms
(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
1.0ms
(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

series571.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
114.0ms
(/ 1 (fma 2.0 i (+ alpha beta)))
130.0ms
(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
196.0ms
(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

simplify1.8s

Counts
146 → 146
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02162503
15072268
214882081
done50002079

prune570.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
0.2b
(/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b
(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
5.6b
(fma (/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
614×times-frac
573×*-un-lft-identity
389×add-sqr-sqrt
352×sqrt-prod
261×add-cube-cbrt
92×distribute-lft-out
64×distribute-lft-out-- difference-of-squares
50×associate-/l*
20×sqrt-div associate-/r/
17×associate-/r*
13×add-exp-log add-cbrt-cube
11×flip3-+ flip-+ div-inv
5×cbrt-undiv div-exp associate-/l/
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg div-sub clear-num
1×flip3-- flip-- fma-udef
Counts
4 → 466
Calls
4 calls:
36.0ms
(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
83.0ms
(/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
24.0ms
(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms
(fma (/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series580.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
110.0ms
(/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
144.0ms
(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
218.0ms
(fma (/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.7s

Counts
478 → 478
Iterations

Useful iterations: done (1.7s)

IterNodesCost
046518827
1105416321
2256215340
done500114583

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.3b
(/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha))
0.5b
(/ 1 (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha)))
5.8b
(fma (/ (/ 1 (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite370.0ms

Algorithm
rewrite-expression-head
Rules
3018×times-frac
2122×*-un-lft-identity
1572×add-sqr-sqrt
1164×add-cube-cbrt
1100×sqrt-prod
275×distribute-lft-out
204×distribute-lft-out-- difference-of-squares
138×associate-/l*
69×associate-/r/
53×associate-/r*
39×div-inv
36×add-exp-log
29×flip3-- flip--
22×div-exp
20×add-cbrt-cube
10×cbrt-undiv
5×pow1
4×expm1-log1p-u rec-exp sqrt-div 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/l/
2×flip3-+ flip-+
1×pow-flip fma-udef inv-pow
Counts
4 → 1321
Calls
4 calls:
121.0ms
(/ (/ 1 (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
22.0ms
(/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha))
42.0ms
(/ 1 (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha)))
0.0ms
(fma (/ (/ 1 (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series835.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(/ (/ 1 (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
247.0ms
(/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha))
266.0ms
(/ 1 (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha)))
101.0ms
(fma (/ (/ 1 (/ (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)) (- beta alpha))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify3.6s

Counts
1333 → 1333
Iterations

Useful iterations: 2 (2.5s)

IterNodesCost
0110461409
1259250813
2477946460
done500046460

prune2.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.9b

regimes239.0ms

Accuracy

0% (0.3b remaining)

Error of 12.1b against oracle of 11.8b and baseline of 12.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01326
11526
done1526

end0.0ms

sample2.4s

Algorithm
intervals
Results
660.0ms6381×body80valid
658.0ms486×body1280valid
358.0ms8000×pre80true
233.0ms574×body640valid
81.0ms324×body320valid
37.0ms235×body160valid