Details

sample145.0ms

Algorithm

intervals

Results

56.0ms	341×	body	80	nan
43.0ms	367×	body	80	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2777
5	1555
4	687
3	260
2	91
1	40
0	20

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
0.1b	(- x (fma (log x) (- x 0.5) 0.91893853320467))
0.3b	(fma (log x) (- x 0.5) 0.91893853320467)
5.0b	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
9×	`times-frac` `prod-diff`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`associate-/r` `fma-neg` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
5.0ms	(- x (fma (log x) (- x 0.5) 0.91893853320467))
0.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
4.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

series882.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
349.0ms	(- x (fma (log x) (- x 0.5) 0.91893853320467))
379.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
98.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

simplify2.5s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
3	3575
2	1013
1	365
0	170

prune804.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.8b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (log x) (- x 0.5) 0.91893853320467)
0.3b	(fma (log x) (- x 0.5) 0.91893853320467)
0.4b	(* (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (- (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
5.0b	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-prod`
72×	`add-sqr-sqrt` `prod-diff`
70×	`*-un-lft-identity`
62×	`add-cube-cbrt`
38×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac` `associate-r`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `flip3-+` `flip3--` `flip-+` `flip--` `associate-/l`
2×	`sub-neg` `associate-l/` `associate-r/` `fma-udef` `distribute-lft-out` `distribute-lft-out--`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 161

Calls

4 calls:

0.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
1.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
79.0ms	(* (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (- (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
4.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

series1.5s

Counts

4 → 12

Calls

4 calls:

388.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
442.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
582.0ms	(* (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (- (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
128.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

simplify6.8s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
1	1456
0	476

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.2b

localize91.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (log x) (- x 0.5) 0.91893853320467)
0.3b	(fma (log x) (- x 0.5) 0.91893853320467)
0.5b	(* (sqrt (fma (log x) (- x 0.5) 0.91893853320467)) (sqrt (fma (log x) (- x 0.5) 0.91893853320467)))
5.0b	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`pow1`
18×	`sqrt-prod`
9×	`times-frac`
8×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `swap-sqr` `add-exp-log`
6×	`associate-r` `associate-l`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `pow-sqr` `associate-/l`
2×	`fma-udef`
1×	`pow2` `cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 100

Calls

4 calls:

0.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
0.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
10.0ms	(* (sqrt (fma (log x) (- x 0.5) 0.91893853320467)) (sqrt (fma (log x) (- x 0.5) 0.91893853320467)))
4.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

404.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
368.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
340.0ms	(* (sqrt (fma (log x) (- x 0.5) 0.91893853320467)) (sqrt (fma (log x) (- x 0.5) 0.91893853320467)))
121.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

simplify1.9s

Counts

112 → 112

Iterations

Iter	Nodes
done	5006
3	1997
2	682
1	293
0	151

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (log x) (- x 0.5) 0.91893853320467)
0.4b	(* (sqrt x) (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
0.4b	(* (- (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
5.0b	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
22×	`associate-l`
21×	`add-cube-cbrt`
14×	`sqrt-prod`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-/r` `associate-/l` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`distribute-lft-neg-out` `cbrt-undiv` `clear-num` `neg-mul-1` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 109

Calls

4 calls:

0.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
35.0ms	(* (sqrt x) (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
70.0ms	(* (- (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
4.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

series1.6s

Counts

4 → 12

Calls

4 calls:

694.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
315.0ms	(* (sqrt x) (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
497.0ms	(* (- (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
111.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

simplify7.3s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
1	1435
0	470

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes684.0ms

Accuracy

94.1% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 6.0b

bsearch134.0ms

Steps

Iters	Range		Point
6	4.2830343312974017e+24	5.509241534777453e+25	4.352031582741585e+24

simplify9.0ms

Iterations

Iter	Nodes
done	43
1	43
0	37

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.9s	11723×	body	80	valid
1.1s	11550×	body	80	nan