Details

sample84.0ms

Algorithm

intervals

Results

27.0ms	382×	body	80	valid
24.0ms	381×	body	80	nan

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4181
4	921
3	265
2	92
1	40
0	20

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.5b

localize36.0ms

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) (/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)) (- 0.91893853320467 x))
0.1b	(fma (log x) (- x 0.5) (/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x))
6.0b	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

0.0ms	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
14.0ms	(+ (fma (log x) (- x 0.5) (/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)) (- 0.91893853320467 x))
0.0ms	(fma (log x) (- x 0.5) (/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x))
4.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

series437.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
147.0ms	(+ (fma (log x) (- x 0.5) (/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)) (- 0.91893853320467 x))
135.0ms	(fma (log x) (- x 0.5) (/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x))
113.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

simplify781.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1375
1	395
0	174

prune787.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 0.5) (log x) (+ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- 0.91893853320467 x)))
0.5b	(* (sqrt x) (sqrt x))
6.0b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)
60.1b	(fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x)))

rewrite33.0ms

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 (- x 0.5) (log x) (+ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- 0.91893853320467 x)))
20.0ms	(* (sqrt x) (sqrt x))
7.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)
0.0ms	(fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(fma (- x 0.5) (log x) (+ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- 0.91893853320467 x)))
37.0ms	(* (sqrt x) (sqrt x))
108.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)
170.0ms	(fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x)))

simplify1.0s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	1675
1	400
0	179

prune862.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize77.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 0.5) (log x) (+ (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)) (- 0.91893853320467 x)))
0.5b	(* (sqrt x) (sqrt x))
6.2b	(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))
60.1b	(fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

0.0ms	(fma (- x 0.5) (log x) (+ (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)) (- 0.91893853320467 x)))
12.0ms	(* (sqrt x) (sqrt x))
12.0ms	(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))
0.0ms	(fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(fma (- x 0.5) (log x) (+ (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)) (- 0.91893853320467 x)))
17.0ms	(* (sqrt x) (sqrt x))
105.0ms	(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))
121.0ms	(fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x)))

simplify1.4s

Counts

121 → 121

Iterations

Iter	Nodes
done	5001
2	2344
1	492
0	199

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ z (/ x z))
0.2b	(* (/ z x) 0.0027777777777778)
0.5b	(* (sqrt x) (sqrt x))
60.1b	(fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 167

Calls

4 calls:

14.0ms	(/ z (/ x z))
24.0ms	(* (/ z x) 0.0027777777777778)
18.0ms	(* (sqrt x) (sqrt x))
0.0ms	(fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ z (/ x z))
35.0ms	(* (/ z x) 0.0027777777777778)
22.0ms	(* (sqrt x) (sqrt x))
148.0ms	(fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x)))

simplify2.2s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	4984
1	700
0	273

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes431.0ms

Accuracy

64.6% (2.1b remaining)

Error of 2.8b against oracle of 0.7b and baseline of 6.5b

bsearch151.0ms

Steps

Iters	Range		Point
8	8.017308199585837e+44	1.4313346338374724e+48	1.1684365911919161e+48

simplify4.0ms

Iterations

Iter	Nodes
done	48
1	48
0	38

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.4s	11827×	body	80	valid
1.2s	11707×	body	80	nan