Details

sample121.0ms

Algorithm

intervals

Results

37.0ms	406×	body	80	nan
33.0ms	363×	body	80	valid

simplify5.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (213.0ms)

Iter	Nodes	Cost
0	20	24
1	40	23
2	92	23
3	263	23
4	576	22
5	1144	22
6	2010	22
7	4222	22
done	5000	22

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(* (- x 0.5) (log x))
3.6b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

62.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
99.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
28.0ms	(* (- x 0.5) (log x))
80.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
598.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
330.0ms	(* (- x 0.5) (log x))
129.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.6s

Counts

126 → 126

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	254	1817
1	605	1715
2	1797	1531
done	5000	1511

prune790.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(fma 0.5 (- (log x)) (- 0.91893853320467 (fma (- (log x)) x x)))
0.2b	(fma (- (log x)) x x)
3.6b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

59.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma 0.5 (- (log x)) (- 0.91893853320467 (fma (- (log x)) x x)))
1.0ms	(fma (- (log x)) x x)
93.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.5s

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
657.0ms	(fma 0.5 (- (log x)) (- 0.91893853320467 (fma (- (log x)) x x)))
716.0ms	(fma (- (log x)) x x)
93.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.3s

Counts

85 → 85

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	179	1399
1	404	1326
2	1229	1184
done	5000	1128

prune556.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (cbrt x)) (- x 0.5)))
0.5b	(cbrt x)
0.5b	(cbrt x)
3.6b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

45.0ms	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (cbrt x)) (- x 0.5)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
89.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (cbrt x)) (- x 0.5)))
301.0ms	(cbrt x)
221.0ms	(cbrt x)
141.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.7s

Counts

132 → 132

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	256	2569
1	684	2128
2	2283	1696
done	5002	1539

prune941.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (pow x 1/3)) (- x 0.5)))
0.5b	(cbrt x)
3.6b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.0b	(pow x 1/3)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+l+` `associate-+r+` `distribute-lft-in`
9×	`times-frac`
8×	`associate-*r/`
7×	`add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `frac-add` `flip--` `log1p-expm1-u`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow` `associate-/r` `associate-/l`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `distribute-rgt-out` `pow-pow` `fma-def` `frac-2neg` `unpow1/3` `pow1/3` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `sqr-pow`

Counts

4 → 127

Calls

4 calls:

53.0ms	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (pow x 1/3)) (- x 0.5)))
2.0ms	(cbrt x)
75.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
4.0ms	(pow x 1/3)

series2.1s

Counts

4 → 12

Calls

4 calls:

1.4s	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (pow x 1/3)) (- x 0.5)))
260.0ms	(cbrt x)
125.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
287.0ms	(pow x 1/3)

simplify1.7s

Counts

139 → 139

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	295	2721
1	776	2198
2	2547	1779
done	5000	1675

prune908.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.3b

regimes502.0ms

Accuracy

85.5% (0.3b remaining)

Error of 4.4b against oracle of 4.1b and baseline of 6.3b

bsearch110.0ms

Steps

Iters	Range		Point
9	4.79102472398497e+62	1.2122981814430234e+69	1.5176050332502085e+66

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	69
1	55	69
done	55	69

end0.0ms

sample2.5s

Algorithm

intervals

Results

813.0ms	11613×	body	80	valid
681.0ms	11565×	body	80	nan