Details

sample84.0ms

Algorithm

intervals

Results

35.0ms

293×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 3 (112.0ms)

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: 28.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma (fma z 3.13060547623 11.1667541262) z t) z a)
0.1b	(fma (fma z 3.13060547623 11.1667541262) z t)
2.7b	(/ 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)

rewrite12.0ms

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 (fma z 3.13060547623 11.1667541262) z t) z a)
0.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
8.0ms	(/ 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)

series1.2s

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma (fma (fma z 3.13060547623 11.1667541262) z t) z a)
53.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
186.0ms	(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
928.0ms	(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)

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	145	1459
1	273	1441
2	633	1279
3	1691	1266
done	5001	1258

prune558.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma z 3.13060547623 11.1667541262) z t)
0.3b	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
2.7b	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
28.2b	(fma (* y (/ 1 (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)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 91

Calls

4 calls:

1.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
13.0ms	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
26.0ms	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
1.0ms	(fma (* y (/ 1 (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)

series1.2s

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
88.0ms	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
137.0ms	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
952.0ms	(fma (* y (/ 1 (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)

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	173	2172
1	358	2001
2	783	1752
3	1951	1745
done	5000	1738

prune538.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

18.2b	(cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
18.2b	(cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
18.2b	(cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
28.2b	(fma (* y (* (* (cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (/ 1 (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)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
25×	`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×	`cbrt-div` `pow1/3` `div-inv`
1×	`fma-udef`

Counts

4 → 82

Calls

4 calls:

4.0ms	(cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
4.0ms	(cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
3.0ms	(cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
0.0ms	(fma (* y (* (* (cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (/ 1 (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:

178.0ms	(cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
196.0ms	(cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
269.0ms	(cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
967.0ms	(fma (* y (* (* (cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (cbrt (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))) (cbrt (/ 1 (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)

simplify1.2s

Counts

94 → 94

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	132	3024
1	243	2895
2	518	2339
3	1424	2286
done	5001	2284

prune646.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

22.5b	(cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))
22.5b	(cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))
22.5b	(cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))
28.2b	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (* (* (cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a)) (cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))) (cbrt (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 3.13060547623 11.1667541262) z t) z a))
1.0ms	(cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))
1.0ms	(cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))
0.0ms	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (* (* (cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a)) (cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))) (cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))) z b) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))
253.0ms	(cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))
287.0ms	(cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))
992.0ms	(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (* (* (cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a)) (cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))) (cbrt (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a))) z b) x)

simplify3.3s

Counts

61 → 61

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	99	1781
1	201	1751
2	461	1330
3	1237	1157
4	3993	1110
done	5000	1107

prune569.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

regimes1.4s

Accuracy

98% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 27.9b

bsearch343.0ms

Steps

Iters	Range		Point
7	9.600036809781282e+47	5.476574644000808e+49	5.0162375809899815e+48
9	-8.007751505722922e+46	-2.6910019437958406e+40	-2.2924083136134216e+44

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	34	58
1	40	49
done	40	49

end0.0ms

sample1.6s

Algorithm

intervals

Results

920.0ms

8893×

body

valid