Details

Time bar (total: 32.8s)

sample54.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
6.0ms256×pre80true

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5000
43214
3509
2114
133
014

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize41.0ms

Local error

Found 3 expressions with local error:

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

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
547×*-un-lft-identity
319×add-sqr-sqrt add-cube-cbrt
114×distribute-lft-out
72×associate-/l*
27×div-inv
19×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
4×associate-/l/
3×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
2×flip3-+ associate-/r/ flip-+
Counts
3 → 404
Calls
3 calls:
23.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
46.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
28.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series621.0ms

Counts
3 → 9
Calls
3 calls:
209.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
297.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
114.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify2.7s

Counts
413 → 413
Iterations
IterNodes
done5006
22871
11135
0500

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.3b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite365.0ms

Algorithm
rewrite-expression-head
Rules
3314×times-frac
2034×*-un-lft-identity
1330×add-sqr-sqrt add-cube-cbrt
352×distribute-lft-out
174×associate-/l*
89×div-inv
76×associate-/r*
64×add-exp-log
44×div-exp
34×add-cbrt-cube
28×associate-/r/
20×cbrt-undiv
6×rec-exp 1-exp
5×pow1
4×expm1-log1p-u clear-num frac-2neg log1p-expm1-u add-log-exp
3×associate-/l/
2×flip3-+ flip-+
1×pow-flip inv-pow
Counts
4 → 1214
Calls
4 calls:
18.0ms
(/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
30.0ms
(/ 1 (/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
120.0ms
(/ (/ 1 (/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
29.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series829.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
254.0ms
(/ 1 (/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
243.0ms
(/ (/ 1 (/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
132.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify4.6s

Counts
1226 → 1226
Iterations
IterNodes
done5000
13635
01405

prune6.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
0.2b
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
3.4b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
3.4b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
420×times-frac
344×sqrt-prod
328×*-un-lft-identity
228×add-sqr-sqrt add-cube-cbrt
50×distribute-lft-out
46×associate-/l*
18×associate-/r* div-inv
12×add-cbrt-cube add-exp-log
6×associate-/l/
4×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp log1p-expm1-u add-log-exp
2×sqrt-undiv flip3-+ sqrt-div flip-+
Counts
4 → 380
Calls
4 calls:
28.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
22.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
24.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
14.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series847.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
334.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
123.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
140.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify3.1s

Counts
392 → 392
Iterations
IterNodes
done5000
34561
21201
1514
0291

prune2.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))))
0.2b
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
3.4b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.4b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
102×add-sqr-sqrt
85×times-frac
80×*-un-lft-identity
59×sqrt-prod
50×add-cube-cbrt
25×associate-*r* associate-*l*
23×add-exp-log
18×add-cbrt-cube
15×unswap-sqr
12×distribute-lft-out
8×pow1 div-exp
7×associate-/l*
6×sqrt-div prod-exp
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×associate-/r* flip3-+ flip-+ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 1-exp hypot-def associate-/l/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 174
Calls
4 calls:
78.0ms
(* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))))
13.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
7.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
7.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series552.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))))
288.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
65.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
82.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify1.8s

Counts
186 → 186
Iterations
IterNodes
done5000
21637
1649
0229

prune1.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes158.0ms

Accuracy

68.7% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 3.7b

bsearch49.0ms

Steps
ItersRangePoint
6
3.98476588440582e+154
3.241544382274341e+155
2.9880490900430075e+155

simplify4.0ms

Iterations
IterNodes
done31
131
024

end0.0ms

sample1.5s

Algorithm
intervals
Results
735.0ms8000×body80valid
557.0ms8000×pre80true