Details

sample52.0ms

Algorithm

intervals

Results

28.0ms

289×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	30	37
1	62	30
2	132	30
3	376	29
4	1053	29
5	3174	29
done	5001	29

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma z 3.13060547623 11.1667541262) z t)
0.1b	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
2.0b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.3b	(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)

rewrite13.0ms

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)
1.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
9.0ms	(/ 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)

series1.3s

Counts

4 → 12

Calls

4 calls:

49.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
42.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
131.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.1s	(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)

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	144	1442
1	272	1423
2	631	1264
3	1689	1254
done	5001	1245

prune620.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
0.1b	(* (fma z 3.13060547623 11.1667541262) z)
2.0b	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.3b	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (+ (* (fma z 3.13060547623 11.1667541262) z) t) z a) z b) x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

0.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
9.0ms	(* (fma z 3.13060547623 11.1667541262) z)
5.0ms	(/ 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 z 3.13060547623 11.1667541262) z) t) z a) z b) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
95.0ms	(* (fma z 3.13060547623 11.1667541262) z)
175.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
865.0ms	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (+ (* (fma z 3.13060547623 11.1667541262) z) t) z a) z b) x)

simplify1.8s

Counts

81 → 81

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	162	1524
1	310	1487
2	800	1323
3	2304	1313
done	5000	1309

prune604.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

16.6b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
16.6b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
16.6b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.3b	(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (fma (fma (+ (* (fma z 3.13060547623 11.1667541262) z) t) z a) z b) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
0.0ms	(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (fma (fma (+ (* (fma z 3.13060547623 11.1667541262) z) t) z a) z b) x)

series1.7s

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
223.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
246.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0s	(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (fma (fma (+ (* (fma z 3.13060547623 11.1667541262) z) t) z a) z b) x)

simplify3.0s

Counts

61 → 61

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	92	1795
1	186	1749
2	448	1258
3	1318	1202
4	4919	1200
done	5000	1200

prune569.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize56.0ms

Local error

Found 4 expressions with local error:

16.6b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
16.6b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
16.6b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.3b	(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (* (* (cbrt (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (cbrt (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))))) (fma (fma (+ (* (fma z 3.13060547623 11.1667541262) z) t) z a) z b) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
0.0ms	(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (* (* (cbrt (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (cbrt (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))))) (fma (fma (+ (* (fma z 3.13060547623 11.1667541262) z) t) z a) z b) x)

series1.9s

Counts

4 → 12

Calls

4 calls:

211.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
224.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
261.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.2s	(fma (/ (/ y (* (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (* (* (cbrt (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (cbrt (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))))) (fma (fma (+ (* (fma z 3.13060547623 11.1667541262) z) t) z a) z b) x)

simplify1.6s

Counts

61 → 61

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	93	2198
1	191	2152
2	479	1577
3	1514	1202
done	5000	1173

prune690.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.3b

regimes1.2s

Accuracy

97.2% (0.8b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 28.1b

bsearch451.0ms

Steps

Iters	Range		Point
9	3362531629907095.5	2.5466853882450202e+20	1.7747029473960237e+20
10	-4.920590848878685e+54	-1.163450456227624e+39	-7.038261497315182e+47

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	33	58
1	40	49
done	40	49

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.2s

8879×

body

valid