Details

sample152.0ms

Algorithm

intervals

Results

63.0ms	401×	body	80	nan
54.0ms	368×	body	80	valid

simplify3.7s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize32.0ms

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)
3.9b	(/ (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` `insert-posit16` `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 → 82

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)

series952.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
377.0ms	(- x (fma (log x) (- x 0.5) 0.91893853320467))
392.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
125.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

simplify2.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	3517
2	1026
1	369
0	174

prune576.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
0.1b	(- (fma (- (log x)) (- x 0.5) x) 0.91893853320467)
0.1b	(fma (- (log x)) (- x 0.5) x)
3.9b	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

rewrite10.0ms

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` `insert-posit16` `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` `associate--l+` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 82

Calls

4 calls:

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

series936.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
378.0ms	(- (fma (- (log x)) (- x 0.5) x) 0.91893853320467)
410.0ms	(fma (- (log x)) (- x 0.5) x)
97.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

simplify2.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	3073
2	882
1	382
0	178

prune599.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

localize56.0ms

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)))
3.9b	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

rewrite31.0ms

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` `insert-posit16` `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 → 104

Calls

4 calls:

1.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
0.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
21.0ms	(* (sqrt (fma (log x) (- x 0.5) 0.91893853320467)) (sqrt (fma (log x) (- x 0.5) 0.91893853320467)))
7.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

391.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
368.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
407.0ms	(* (sqrt (fma (log x) (- x 0.5) 0.91893853320467)) (sqrt (fma (log x) (- x 0.5) 0.91893853320467)))
98.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

simplify1.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	5002
3	2059
2	704
1	317
0	154

prune627.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (fma (- (log x)) (- x 0.5) x) 0.91893853320467)
0.1b	(fma (- (log x)) (- x 0.5) x)
2.0b	(/ (/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) (sqrt x)) (sqrt x))
2.4b	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) (sqrt x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
165×	`add-sqr-sqrt` `*-un-lft-identity`
163×	`add-cube-cbrt`
144×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff` `div-inv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`clear-num` `frac-2neg` `fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares` `associate-/l/`

Counts

4 → 261

Calls

4 calls:

8.0ms	(- (fma (- (log x)) (- x 0.5) x) 0.91893853320467)
0.0ms	(fma (- (log x)) (- x 0.5) x)
22.0ms	(/ (/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) (sqrt x)) (sqrt x))
8.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) (sqrt x))

series1.1s

Counts

4 → 12

Calls

4 calls:

476.0ms	(- (fma (- (log x)) (- x 0.5) x) 0.91893853320467)
433.0ms	(fma (- (log x)) (- x 0.5) x)
109.0ms	(/ (/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) (sqrt x)) (sqrt x))
120.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) (sqrt x))

simplify2.1s

Counts

273 → 273

Iterations

Iter	Nodes
done	5003
2	2103
1	884
0	387

prune1.7s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 1.0b

regimes492.0ms

Accuracy

64.7% (1.9b remaining)

Error of 2.5b against oracle of 0.6b and baseline of 6.0b

bsearch108.0ms

Steps

Iters	Range		Point
7	1.424909669384806e+136	5.386384588899324e+137	2.010811705498022e+137

simplify6.0ms

Iterations

Iter	Nodes
done	40
1	40
0	36

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.3s	11823×	body	80	valid
1.9s	11750×	body	80	nan