Details

Time bar (total: 14.6s)

sample117.0ms

Algorithm
intervals
Results
68.0ms291×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
03037
16230
213230
338629
4130129
done500029

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma z 3.13060547623 11.1667541262) z t)
0.1b
(fma (fma (fma z 3.13060547623 11.1667541262) z t) z a)
2.2b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
27.0b
(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)

rewrite16.0ms

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 (fma z 3.13060547623 11.1667541262) z t)
1.0ms
(fma (fma (fma z 3.13060547623 11.1667541262) z t) z a)
11.0ms
(/ 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 (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

series1.8s

Counts
4 → 12
Calls
4 calls:
45.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
92.0ms
(fma (fma (fma z 3.13060547623 11.1667541262) z t) z a)
183.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.5s
(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)

simplify2.2s

Counts
71 → 71
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01451459
12781441
28371288
339231276
done50001267

prune602.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 2 expressions with local error:

3.3b
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
6.7b
(/ t (pow z 2))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
8×associate-/r*
7×add-exp-log
4×add-cbrt-cube unpow2 sqr-pow
3×div-exp associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num fma-udef div-inv
Counts
2 → 61
Calls
2 calls:
0.0ms
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
10.0ms
(/ t (pow z 2))

series95.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
26.0ms
(/ t (pow z 2))

simplify726.0ms

Counts
67 → 67
Iterations

Useful iterations: done (723.0ms)

IterNodesCost
0111726
1201677
2757577
done5000575

prune321.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (/ t z) z)
3.3b
(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
44×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×associate-/l*
7×add-exp-log add-cbrt-cube
5×div-inv
3×cbrt-undiv div-exp associate-/r*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×frac-2neg clear-num fma-udef associate-/l/
Counts
2 → 82
Calls
2 calls:
30.0ms
(/ (/ t z) z)
0.0ms
(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

series119.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(/ (/ t z) z)
87.0ms
(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

simplify1000.0ms

Counts
88 → 88
Iterations

Useful iterations: done (997.0ms)

IterNodesCost
01621054
13771005
21718924
done5001912

prune430.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
6.1b
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
6.1b
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
27.0b
(fma (* (/ 1 (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ y (sqrt (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)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 81
Calls
4 calls:
11.0ms
(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
3.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
3.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(fma (* (/ 1 (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ y (sqrt (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)

series1.1s

Counts
4 → 12
Calls
4 calls:
250.0ms
(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
174.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
138.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
569.0ms
(fma (* (/ 1 (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ y (sqrt (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)

simplify644.0ms

Counts
93 → 93
Iterations

Useful iterations: done (638.0ms)

IterNodesCost
01592394
13242226
210422041
done50011852

prune543.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

regimes990.0ms

Accuracy

97.3% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 27.2b

bsearch4.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
045133
164133
done64133

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.7s8947×body80valid