Details

sample137.0ms

Algorithm

intervals

Results

51.0ms	381×	body	80	valid
43.0ms	455×	body	80	nan

simplify3.2s

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.7b

localize63.0ms

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)

rewrite182.0ms

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:

15.0ms	(- (* (- x 0.5) (log x)) x)
83.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
32.0ms	(* (- x 0.5) (log x))
48.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

653.0ms	(- (* (- x 0.5) (log x)) x)
649.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
343.0ms	(* (- x 0.5) (log x))
110.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.8s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	2726
1	636
0	241

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ y 0.0007936500793651) z)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.4b	(fma (log x) (- x 0.5) (- 0.91893853320467 x))
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

18.0ms	(* (+ y 0.0007936500793651) z)
59.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- 0.91893853320467 x))
71.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series704.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (+ y 0.0007936500793651) z)
79.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
453.0ms	(fma (log x) (- x 0.5) (- 0.91893853320467 x))
120.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	1839
1	462
0	192

prune805.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize99.0ms

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)

rewrite87.0ms

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)
80.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series969.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(cbrt x)
229.0ms	(cbrt x)
330.0ms	(cbrt x)
130.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	823
1	232
0	101

prune876.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize108.0ms

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)

rewrite71.0ms

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)
55.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
11.0ms	(pow (/ 1 x) -1/3)

series962.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(cbrt x)
284.0ms	(cbrt x)
150.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
297.0ms	(pow (/ 1 x) -1/3)

simplify1.1s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
2	1521
1	461
0	174

prune712.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes931.0ms

Accuracy

94.2% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 5.9b

bsearch98.0ms

Steps

Iters	Range		Point
6	0.6893947674185039	4.9803363081918155	4.890764603747723

simplify8.0ms

Iterations

Iter	Nodes
done	49
1	49
0	37

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.7s	11627×	body	80	valid
1.5s	11680×	body	80	nan