Details

Time bar (total: 24.7s)

sample55.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
6.0ms256×pre80true

simplify2.4s

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
0.0b
(/ (/ (+ 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))))
2.2b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
551×*-un-lft-identity
321×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
72×associate-/l*
27×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
6×add-log-exp
4×expm1-log1p-u pow1 log1p-expm1-u associate-/l/
3×clear-num fma-def frac-2neg flip3-+ flip-+
2×associate-/r/
1×+-commutative associate-+r+ sum-log fma-udef
Counts
4 → 422
Calls
4 calls:
10.0ms
(+ 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))) (fma 2.0 1.0 (+ beta alpha)))
52.0ms
(/ (/ (/ (+ 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))))
19.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series644.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
248.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
240.0ms
(/ (/ (/ (+ 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))))
124.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify3.4s

Counts
434 → 434
Iterations
IterNodes
done5001
22978
11172
0516

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
0.0b
(expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
0.1b
(/ (log1p (expm1 (/ (/ (+ 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))))
2.2b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
24×times-frac
22×add-sqr-sqrt add-cube-cbrt
8×add-cbrt-cube add-exp-log distribute-lft-out
7×associate-/r* associate-/l*
5×log1p-expm1-u
4×expm1-log1p-u pow1 add-log-exp
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+ div-inv associate-/l/
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
4 → 92
Calls
4 calls:
0.0ms
(log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
0.0ms
(expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
23.0ms
(/ (log1p (expm1 (/ (/ (+ 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))))
26.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series1.2s

Counts
4 → 12
Calls
4 calls:
334.0ms
(log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
409.0ms
(expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
328.0ms
(/ (log1p (expm1 (/ (/ (+ 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))))
121.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify1.3s

Counts
104 → 104
Iterations
IterNodes
done5000
21297
1414
0186

prune801.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
0.0b
(expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
0.1b
(* (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))) (/ 1 (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
2.2b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
29×add-sqr-sqrt
26×times-frac
22×add-cube-cbrt
18×associate-*r*
15×add-exp-log
11×add-cbrt-cube
7×distribute-lft-out
6×pow1
5×log1p-expm1-u
4×expm1-log1p-u prod-exp associate-/l* add-log-exp
3×associate-/r* div-exp associate-*l* unswap-sqr
2×cbrt-undiv flip3-+ associate-/r/ cbrt-unprod flip-+ div-inv associate-/l/
1×rec-exp log1p-udef expm1-log1p clear-num frac-2neg 1-exp pow-prod-down log1p-expm1 associate-*r/ un-div-inv *-commutative expm1-udef
Counts
4 → 100
Calls
4 calls:
0.0ms
(log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
1.0ms
(expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
44.0ms
(* (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))) (/ 1 (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
24.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series1.1s

Counts
4 → 12
Calls
4 calls:
267.0ms
(log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
392.0ms
(expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
271.0ms
(* (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))) (/ 1 (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
133.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify1.6s

Counts
112 → 112
Iterations
IterNodes
done5001
21749
1508
0211

prune758.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (sqrt (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))))
0.1b
(/ (sqrt (log1p (expm1 (/ (/ (+ 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))) (sqrt (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))))))
2.2b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
2.2b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
384×times-frac
316×*-un-lft-identity
202×add-sqr-sqrt add-cube-cbrt
186×sqrt-prod
57×distribute-lft-out
40×associate-/r*
18×associate-/l*
15×add-cbrt-cube add-exp-log
11×div-inv
6×cbrt-undiv div-exp associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
3×flip3-+ flip-+
1×associate-/r/
Counts
4 → 339
Calls
4 calls:
16.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (sqrt (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))))
21.0ms
(/ (sqrt (log1p (expm1 (/ (/ (+ 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))) (sqrt (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))))))
15.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
21.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.0s
(/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (sqrt (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))))
304.0ms
(/ (sqrt (log1p (expm1 (/ (/ (+ 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))) (sqrt (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))))))
139.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
152.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify2.4s

Counts
351 → 351
Iterations
IterNodes
done5005
22473
1939
0372

prune2.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

regimes239.0ms

Accuracy

40.8% (1.5b remaining)

Error of 2.8b against oracle of 1.3b and baseline of 3.8b

bsearch147.0ms

Steps
ItersRangePoint
9
2.151915573351709e+83
2.9240802407216853e+91
2.7950690928549397e+91

simplify6.0ms

Iterations
IterNodes
done33
133
026

end0.0ms

sample1.5s

Algorithm
intervals
Results
964.0ms8000×body80valid
250.0ms8000×pre80true