Details

Time bar (total: 18.0s)

sample32.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
4.0ms256×pre80true

simplify644.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01435
13335
211931
359331
done500131

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
0.0b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
4.1b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite168.0ms

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-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg flip3-+ clear-num flip-+
2×associate-/r/
1×+-commutative associate-+l+ sum-log fma-udef
Counts
4 → 422
Calls
4 calls:
12.0ms
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
28.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
54.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
22.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series589.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
216.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
236.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
101.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify816.0ms

Counts
434 → 434
Iterations

Useful iterations: done (787.0ms)

IterNodesCost
051620618
1132520002
done500019199

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
0.0b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (expm1 (log1p (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
4.1b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
120×times-frac
111×*-un-lft-identity
71×add-sqr-sqrt add-cube-cbrt
23×associate-/l*
20×distribute-lft-out
13×add-exp-log add-cbrt-cube
10×associate-/r*
7×div-inv
5×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/l/
2×flip3-+ associate-/r/ flip-+ expm1-udef
1×expm1-log1p div-sub
Counts
4 → 166
Calls
4 calls:
1.0ms
(expm1 (log1p (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
35.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
22.0ms
(/ (expm1 (log1p (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
21.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series1.2s

Counts
4 → 12
Calls
4 calls:
446.0ms
(expm1 (log1p (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
207.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
455.0ms
(/ (expm1 (log1p (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
140.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.6s

Counts
178 → 178
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02616323
16206045
228115621
done50025483

prune762.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))))
0.1b
(* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
0.1b
(/ (expm1 (log1p (* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
4.1b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
61×*-un-lft-identity
54×add-sqr-sqrt
52×times-frac
37×add-cube-cbrt
30×add-exp-log
20×add-cbrt-cube
16×associate-*l*
13×associate-*r*
11×distribute-lft-out
10×div-exp
8×prod-exp
7×associate-/r* associate-/l*
6×pow1 cbrt-undiv unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
2×rec-exp frac-2neg flip3-+ 1-exp clear-num associate-/r/ flip-+ associate-/l/ expm1-udef
1×frac-times expm1-log1p div-sub associate-*r/ pow-prod-down associate-*l/ un-div-inv *-commutative
Counts
4 → 144
Calls
4 calls:
0.0ms
(expm1 (log1p (* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))))
78.0ms
(* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
23.0ms
(/ (expm1 (log1p (* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
26.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series1.2s

Counts
4 → 12
Calls
4 calls:
476.0ms
(expm1 (log1p (* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))))
195.0ms
(* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
391.0ms
(/ (expm1 (log1p (* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
135.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify3.0s

Counts
156 → 156
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02405151
16524853
238224220
done50004207

prune676.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
0.2b
(/ (sqrt (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
4.1b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
4.1b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite169.0ms

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-exp-log add-cbrt-cube
6×associate-/l/
4×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u add-log-exp
2×sqrt-undiv flip3-+ sqrt-div flip-+
Counts
4 → 380
Calls
4 calls:
37.0ms
(/ (sqrt (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
27.0ms
(/ (sqrt (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
48.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
33.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series803.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(/ (sqrt (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
290.0ms
(/ (sqrt (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
136.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
131.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.2s

Counts
392 → 392
Iterations

Useful iterations: done (1.2s)

IterNodesCost
029115958
151314972
2201714344
done500014336

prune1.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.6b

regimes103.0ms

Accuracy

54.5% (1.2b remaining)

Error of 2.4b against oracle of 1.1b and baseline of 3.8b

bsearch42.0ms

Steps
ItersRangePoint
4
5.64112133829597e+173
1.045369472320571e+174
6.632569412339182e+173

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02149
12449
done2449

end0.0ms

sample1.4s

Algorithm
intervals
Results
958.0ms8000×body80valid
163.0ms8000×pre80true