Details

sample102.0ms

Algorithm

intervals

Results

29.0ms	381×	body	80	valid
28.0ms	455×	body	80	nan

simplify3.6s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (- x 0.5) (log x)) x)
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(* (- x 0.5) (log x))
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

29.0ms	(- (* (- x 0.5) (log x)) x)
73.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
36.0ms	(* (- x 0.5) (log x))
68.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.9s

Counts

4 → 12

Calls

4 calls:

681.0ms	(- (* (- x 0.5) (log x)) x)
717.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
380.0ms	(* (- x 0.5) (log x))
114.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.6s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	1834
1	628
0	241

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(- 0.91893853320467 (fma 0.5 (log x) x))
0.2b	(fma (log x) x (- 0.91893853320467 (fma 0.5 (log x) x)))
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

43.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
10.0ms	(- 0.91893853320467 (fma 0.5 (log x) x))
0.0ms	(fma (log x) x (- 0.91893853320467 (fma 0.5 (log x) x)))
64.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
288.0ms	(- 0.91893853320467 (fma 0.5 (log x) x))
711.0ms	(fma (log x) x (- 0.91893853320467 (fma 0.5 (log x) x)))
141.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.5s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
2	1482
1	492
0	216

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.3b

localize84.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `pow1/3` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
58.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series842.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(cbrt x)
253.0ms	(cbrt x)
233.0ms	(cbrt x)
129.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.2s

Counts

82 → 82

Iterations

Iter	Nodes
done	5019
3	2278
2	654
1	232
0	101

prune821.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize103.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
4.9b	(pow (/ 1 x) -1/3)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
13×	`unpow-prod-down`
11×	`add-exp-log`
6×	`cbrt-prod` `pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `pow-pow` `div-exp` `associate-/l`
2×	`pow1/3` `div-inv` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `pow-flip` `inv-pow` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
67.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
6.0ms	(pow (/ 1 x) -1/3)

series958.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt x)
301.0ms	(cbrt x)
145.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
246.0ms	(pow (/ 1 x) -1/3)

simplify2.1s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
3	3786
2	1235
1	451
0	174

prune977.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes1.1s

Accuracy

96.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 5.9b

bsearch123.0ms

Steps

Iters	Range		Point
7	10993104339.866386	1528168778729.1204	21506604914.31418

simplify10.0ms

Iterations

Iter	Nodes
done	63
1	63
0	47

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.8s	11680×	body	80	nan
1.7s	11627×	body	80	valid