Details

sample64.0ms

Algorithm

intervals

Results

20.0ms	383×	body	80	valid
19.0ms	421×	body	80	nan

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (94.0ms)

Iter	Nodes	Cost
0	20	24
1	40	23
2	91	23
3	213	23
4	497	22
5	1049	22
6	1800	22
7	4349	22
done	5000	22

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ y 0.0007936500793651) z)
0.1b	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b	(fma (log x) (- x 0.5) (+ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- 0.91893853320467 x)))
5.0b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

10.0ms	(* (+ y 0.0007936500793651) z)
0.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.0ms	(fma (log x) (- x 0.5) (+ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- 0.91893853320467 x)))
2.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series299.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (+ y 0.0007936500793651) z)
40.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
142.0ms	(fma (log x) (- x 0.5) (+ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- 0.91893853320467 x)))
86.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify2.0s

Counts

84 → 84

Iterations

Useful iterations: 3 (838.0ms)

Iter	Nodes	Cost
0	156	1365
1	337	1339
2	938	1188
3	3039	1167
done	5000	1167

prune342.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b	(+ (* (log x) (- x 0.5)) (+ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- 0.91893853320467 x)))
0.2b	(* (log x) (- x 0.5))
5.0b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
38×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
13×	`add-log-exp`
12×	`frac-add`
10×	`associate-*r/`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `flip3--` `flip--`
5×	`associate-r` `sum-log`
4×	`expm1-log1p-u` `sub-neg` `associate-l` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-+r-`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `fma-def` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

0.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
48.0ms	(+ (* (log x) (- x 0.5)) (+ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- 0.91893853320467 x)))
15.0ms	(* (log x) (- x 0.5))
2.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series544.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
147.0ms	(+ (* (log x) (- x 0.5)) (+ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- 0.91893853320467 x)))
269.0ms	(* (log x) (- x 0.5))
84.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify1.4s

Counts

146 → 146

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	305	3721
1	828	3246
2	3175	3007
done	5000	2971

prune569.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log x) (- x 0.5))
0.2b	(* (log x) (- x 0.5))
0.5b	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
5.0b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

59×	`pow1`
54×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
44×	`add-cube-cbrt`
36×	`prod-diff`
28×	`sqrt-pow1`
22×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
18×	`associate-*r/`
14×	`associate-r`
12×	`add-exp-log` `sqrt-div` `associate-l` `add-cbrt-cube`
10×	`pow1/2` `pow-prod-up`
9×	`times-frac`
8×	`flip3--` `flip--`
6×	`pow-sqr`
4×	`expm1-log1p-u` `frac-times` `sub-neg` `swap-sqr` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `associate-/r` `-commutative` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`associate-*l/` `log-pow` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `clear-num` `rem-square-sqrt` `div-inv`

Counts

4 → 182

Calls

4 calls:

12.0ms	(* (log x) (- x 0.5))
13.0ms	(* (log x) (- x 0.5))
28.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
2.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series884.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(* (log x) (- x 0.5))
279.0ms	(* (log x) (- x 0.5))
249.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
80.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify1.1s

Counts

194 → 194

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	340	3541
1	771	2796
2	2571	2457
done	5000	2411

prune614.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (log x) (- x 0.5) (+ (* (/ 1 (sqrt x)) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))) (- 0.91893853320467 x)))
0.2b	(/ 1 (sqrt x))
2.3b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))
3.1b	(* (/ 1 (sqrt x)) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
94×	`times-frac`
66×	`*-un-lft-identity`
60×	`add-cube-cbrt`
53×	`sqrt-prod`
32×	`add-exp-log`
22×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `prod-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 183

Calls

4 calls:

0.0ms	(fma (log x) (- x 0.5) (+ (* (/ 1 (sqrt x)) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))) (- 0.91893853320467 x)))
3.0ms	(/ 1 (sqrt x))
3.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))
27.0ms	(* (/ 1 (sqrt x)) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(fma (log x) (- x 0.5) (+ (* (/ 1 (sqrt x)) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))) (- 0.91893853320467 x)))
31.0ms	(/ 1 (sqrt x))
90.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))
97.0ms	(* (/ 1 (sqrt x)) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)))

simplify1.5s

Counts

195 → 195

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	268	4129
1	698	3807
2	2113	3240
done	5000	3214

prune615.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

regimes278.0ms

Accuracy

85.8% (0.3b remaining)

Error of 4.1b against oracle of 3.8b and baseline of 6.1b

bsearch306.0ms

Steps

Iters	Range		Point
7	3.461551022885064e+38	5.676441523312848e+39	5.227246909598967e+38

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	75
1	53	75
done	53	75

end0.0ms

sample1.7s

Algorithm

intervals

Results

637.0ms	11754×	body	80	valid
544.0ms	11519×	body	80	nan