Details

sample100.0ms

Algorithm

intervals

Results

47.0ms

287×

body

valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	30	37
1	62	30
2	132	30
3	386	29
4	1301	29
done	5000	29

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
0.0b	(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))
27.9b	(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)

rewrite17.0ms

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:

8.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
0.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
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)

series1.4s

Counts

4 → 12

Calls

4 calls:

50.0ms	(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
51.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
176.0ms	(/ 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)

simplify2.2s

Counts

71 → 71

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	144	1442
1	277	1423
2	833	1273
3	3905	1261
done	5001	1252

prune543.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma z 3.13060547623 11.1667541262) z t)
0.1b	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
2.8b	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
27.9b	(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)

rewrite29.0ms

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)
7.0ms	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
16.0ms	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
0.0ms	(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:

34.0ms	(fma (fma z 3.13060547623 11.1667541262) z t)
104.0ms	(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
140.0ms	(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
925.0ms	(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)

simplify768.0ms

Counts

103 → 103

Iterations

Useful iterations: done (764.0ms)

Iter	Nodes	Cost
0	173	2172
1	379	2070
2	1380	1767
done	5001	1752

prune659.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

localize64.0ms

Local error

Found 4 expressions with local error:

18.2b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
18.2b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
18.2b	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
27.9b	(fma (* y (* (/ 1 (* (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)))) (/ 1 (cbrt (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)

rewrite6.0ms

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))
2.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms	(fma (* y (* (/ 1 (* (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)))) (/ 1 (cbrt (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:

161.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
159.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
199.0ms	(cbrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.1s	(fma (* y (* (/ 1 (* (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)))) (/ 1 (cbrt (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)

simplify2.1s

Counts

61 → 61

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	93	1834
1	192	1801
2	556	1566
3	2609	1224
done	5004	1200

prune580.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 2 expressions with local error:

3.1b	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
8.6b	(/ t (pow z 2))

rewrite11.0ms

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)
8.0ms	(/ t (pow z 2))

series112.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
35.0ms	(/ t (pow z 2))

simplify643.0ms

Counts

67 → 67

Iterations

Useful iterations: done (640.0ms)

Iter	Nodes	Cost
0	111	726
1	201	677
2	757	577
done	5000	575

prune215.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.6b

regimes1.1s

Accuracy

96.6% (1.0b remaining)

Error of 1.3b against oracle of 0.3b and baseline of 28.2b

bsearch356.0ms

Steps

Iters	Range		Point
9	1.6514850353937772e+35	3.7930850735237604e+42	4.944373784077883e+39
9	-3.586309662752634e+69	-3.562494867365608e+64	-3.605396592194328e+64

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	59
1	43	50
done	43	50

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s

8823×

body

valid