Details

Time bar (total: 52.9s)

sample57.0ms

Algorithm
intervals
Results
28.0ms256×body80valid
6.0ms256×pre80true

simplify4.6s

Counts
1 → 1
Iterations
IterNodes
done5000
43193
3514
2114
133
014

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
3.4b
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
586×times-frac
360×*-un-lft-identity
272×add-sqr-sqrt add-cube-cbrt
59×associate-/l*
44×distribute-lft-out
27×div-inv
19×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×associate-/r/ associate-/l/
1×flip3-+ flip-+
Counts
3 → 341
Calls
3 calls:
34.0ms
(/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
67.0ms
(/ (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
11.0ms
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta)))

series935.0ms

Counts
3 → 9
Calls
3 calls:
364.0ms
(/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
393.0ms
(/ (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
177.0ms
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta)))

simplify3.9s

Counts
350 → 350
Iterations
IterNodes
done5002
22746
11089
0493

prune3.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
0.0b
(* (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
0.1b
(/ (* (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
3.4b
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
53×add-sqr-sqrt
47×times-frac
42×*-un-lft-identity
38×add-cbrt-cube
36×add-cube-cbrt
28×div-exp
16×prod-exp
15×cbrt-undiv
13×associate-*r* associate-*l*
10×associate-/r*
8×cbrt-unprod
7×pow1 associate-/l*
6×unswap-sqr
5×rec-exp 1-exp div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/ associate-/r/ un-div-inv distribute-lft-out
1×pow-flip flip3-+ pow-prod-down *-commutative flip-+ inv-pow
Counts
4 → 162
Calls
4 calls:
9.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
51.0ms
(* (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
48.0ms
(/ (* (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
10.0ms
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta)))

series909.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
342.0ms
(* (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
327.0ms
(/ (* (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
162.0ms
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (fma 1.0 2.0 (+ alpha beta)))

simplify3.7s

Counts
174 → 174
Iterations
IterNodes
done5013
22063
1613
0229

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
0.1b
(/ (* (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
0.8b
(/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
3.3b
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta))))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
573×times-frac
367×add-sqr-sqrt
299×*-un-lft-identity
288×add-cube-cbrt
279×sqrt-prod
136×associate-*l*
103×add-exp-log
61×add-cbrt-cube
53×div-exp
29×cbrt-undiv
26×associate-/l*
24×prod-exp
21×unswap-sqr
18×div-inv
16×associate-/r*
13×associate-*r*
12×cbrt-unprod
6×pow1 rec-exp 1-exp
5×associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/ associate-/r/ un-div-inv distribute-lft-out
1×flip3-+ pow-prod-down *-commutative flip-+
Counts
4 → 468
Calls
4 calls:
175.0ms
(* (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
82.0ms
(/ (* (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
47.0ms
(/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
13.0ms
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta))))

series1.0s

Counts
4 → 12
Calls
4 calls:
304.0ms
(* (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
346.0ms
(/ (* (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
170.0ms
(/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
219.0ms
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta))))

simplify5.9s

Counts
480 → 480
Iterations
IterNodes
done5000
24852
11466
0500

prune4.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.1b

localize110.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
1.4b
(/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (* (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
1.5b
(* (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (* (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))) (/ (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
3.3b
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
1966×times-frac
1054×add-sqr-sqrt
964×*-un-lft-identity
784×add-cube-cbrt
580×associate-*r*
393×sqrt-prod
356×cbrt-prod
185×add-exp-log
104×div-exp
90×add-cbrt-cube
82×distribute-lft-out
64×cbrt-undiv div-inv
60×unswap-sqr
44×prod-exp
38×associate-/l*
34×associate-*l*
30×cbrt-unprod
26×cbrt-div
18×associate-/r/
13×flip3-+ associate-/r* flip-+
10×pow1
9×frac-times
6×rec-exp 1-exp
5×associate-*r/ associate-*l/
4×expm1-log1p-u log1p-expm1-u add-log-exp pow-div
3×frac-2neg clear-num
2×pow-flip sqrt-pow1 pow1/2 associate-/l/ inv-pow
1×pow-prod-down *-commutative
Counts
4 → 973
Calls
4 calls:
27.0ms
(/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
61.0ms
(/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (* (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
942.0ms
(* (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (* (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))) (/ (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
14.0ms
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta))))

series1.2s

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
578.0ms
(/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (* (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
339.0ms
(* (/ (/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (* (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))) (/ (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
186.0ms
(/ (fma alpha beta (+ (+ alpha beta) 1.0)) (sqrt (fma 1.0 2.0 (+ alpha beta))))

simplify7.5s

Counts
985 → 985
Iterations
IterNodes
done5000
14677
01341

prune9.7s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.1b

regimes277.0ms

Accuracy

52.6% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.7b

bsearch140.0ms

Steps
ItersRangePoint
7
1.0879765129995242e+214
3.856056958176191e+215
1.8833927498580965e+214

simplify19.0ms

Iterations
IterNodes
done42
142
032

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.1s8000×body80valid
288.0ms8000×pre80true