Details

Time bar (total: 17.9s)

sample60.0ms

Algorithm
intervals
Results
26.0ms275×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
03037
16230
213230
338629
4130129
done500029

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.4b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma z 3.13060547623 11.1667541262) z t)
0.1b
(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
3.8b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
28.2b
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 59
Calls
4 calls:
0.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
0.0ms
(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
6.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
0.0ms
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

series1.6s

Counts
4 → 12
Calls
4 calls:
43.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
140.0ms
(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
172.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.2s
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

simplify2.7s

Counts
71 → 71
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01451496
12761478
28321320
339961308
done50001301

prune938.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ t (pow z 2)) 3.13060547623)
4.0b
(fma y (+ (/ t (pow z 2)) 3.13060547623) x)
7.0b
(/ t (pow z 2))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
37×*-un-lft-identity
35×add-sqr-sqrt add-cube-cbrt
28×fma-def
21×unpow-prod-down
8×add-exp-log associate-/r*
7×unpow2 sqr-pow
5×add-cbrt-cube add-log-exp
3×pow1 expm1-log1p-u div-exp log1p-expm1-u associate-/l*
2×div-inv
1×cbrt-undiv +-commutative pow-to-exp frac-2neg flip3-+ pow-exp clear-num sum-log flip-+ fma-udef distribute-lft-out
Counts
3 → 103
Calls
3 calls:
56.0ms
(+ (/ t (pow z 2)) 3.13060547623)
0.0ms
(fma y (+ (/ t (pow z 2)) 3.13060547623) x)
13.0ms
(/ t (pow z 2))

series172.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(+ (/ t (pow z 2)) 3.13060547623)
83.0ms
(fma y (+ (/ t (pow z 2)) 3.13060547623) x)
42.0ms
(/ t (pow z 2))

simplify694.0ms

Counts
112 → 112
Iterations

Useful iterations: done (691.0ms)

IterNodesCost
0133915
1268852
21010746
done5001742

prune682.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (/ 1 (pow z (/ 2 2))) (/ t (pow z (/ 2 2))) 3.13060547623)
4.0b
(fma y (fma (/ 1 (pow z (/ 2 2))) (/ t (pow z (/ 2 2))) 3.13060547623) x)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma (/ 1 (pow z (/ 2 2))) (/ t (pow z (/ 2 2))) 3.13060547623)
0.0ms
(fma y (fma (/ 1 (pow z (/ 2 2))) (/ t (pow z (/ 2 2))) 3.13060547623) x)

series104.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(fma (/ 1 (pow z (/ 2 2))) (/ t (pow z (/ 2 2))) 3.13060547623)
69.0ms
(fma y (fma (/ 1 (pow z (/ 2 2))) (/ t (pow z (/ 2 2))) 3.13060547623) x)

simplify688.0ms

Counts
26 → 26
Iterations

Useful iterations: done (687.0ms)

IterNodesCost
042537
170433
2195265
3853262
done5001259

prune233.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma z (fma z 3.13060547623 11.1667541262) t)
0.1b
(fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b)
3.8b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
28.2b
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b) x)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 59
Calls
4 calls:
1.0ms
(fma z (fma z 3.13060547623 11.1667541262) t)
1.0ms
(fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b)
10.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b) x)

series1.3s

Counts
4 → 12
Calls
4 calls:
54.0ms
(fma z (fma z 3.13060547623 11.1667541262) t)
115.0ms
(fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b)
162.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
971.0ms
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma z (fma z 3.13060547623 11.1667541262) t) z a) z b) x)

simplify2.1s

Counts
71 → 71
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01451496
12761478
28321320
339961308
done50001301

prune752.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes1.5s

Accuracy

96.5% (0.9b remaining)

Error of 1.3b against oracle of 0.3b and baseline of 27.2b

bsearch342.0ms

Steps
ItersRangePoint
10
5.108618926184325e+61
1.897770192728618e+77
5.20472607429749e+61
8
-5.988346208256979e+56
-1.4651214872879984e+53
-1.4875640530208235e+53

simplify8.0ms

Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
04066
14462
24658
34858
done4858

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.7s8898×body80valid