Details

sample110.0ms

Algorithm

intervals

Results

31.0ms	60×	body	10240	exit
24.0ms	48×	body	1280	valid
12.0ms	49×	body	640	valid
6.0ms	114×	body	80	valid
4.0ms	4×	body	2560	valid
4.0ms	26×	body	320	valid
2.0ms	78×	body	80	nan
2.0ms	16×	body	160	valid
1.0ms	5×	body	1280	nan
1.0ms	6×	body	640	nan
1.0ms	7×	body	320	nan
0.0ms	1×	body	160	nan

simplify199.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	33	7
2	49	7
3	71	7
4	93	7
5	180	7
6	232	7
7	411	7
8	710	7
9	1092	7
10	1240	7
11	1558	7
12	4191	7
13	5001	7
done	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.9b	(log (+ (- 1.0 y) (* y (exp z))))
2.9b	(+ (- 1.0 y) (* y (exp z)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate-+l+` `div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

11.0ms	(* y (exp z))
50.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
20.0ms	(log (+ (- 1.0 y) (* y (exp z))))
26.0ms	(+ (- 1.0 y) (* y (exp z)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
161.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
76.0ms	(log (+ (- 1.0 y) (* y (exp z))))
36.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify47.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	452	795
1	1740	733
2	5001	726
done	5001	726

prune272.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
0.0b	(* 0.5 (pow z 2))
2.6b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.5b	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`associate-r`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-l` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 89

Calls

4 calls:

9.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
11.0ms	(* 0.5 (pow z 2))
24.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
35.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

series306.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
25.0ms	(* 0.5 (pow z 2))
88.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
122.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

simplify59.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	415	800
1	1832	721
2	5001	715
done	5001	715

prune325.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
0.0b	(* 0.5 (pow z 2))
2.6b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.6b	(* (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (/ 1 t))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
20×	`add-exp-log`
18×	`*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`add-cbrt-cube`
11×	`times-frac`
9×	`associate-l`
8×	`pow1` `prod-exp` `unswap-sqr`
6×	`add-log-exp`
4×	`unpow-prod-down` `flip3-+` `cbrt-unprod` `flip-+`
3×	`associate-r/` `-commutative`
2×	`frac-times` `div-exp` `pow-prod-down` `associate-*l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rec-exp` `distribute-lft-in` `1-exp` `pow-exp` `sum-log` `un-div-inv` `div-inv`

Counts

4 → 100

Calls

4 calls:

9.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
11.0ms	(* 0.5 (pow z 2))
27.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
26.0ms	(* (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (/ 1 t))

series317.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
31.0ms	(* 0.5 (pow z 2))
89.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
123.0ms	(* (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (/ 1 t))

simplify75.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	526	909
1	2623	809
2	5001	797
done	5001	797

prune353.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
1.8b	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt t))
2.6b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
3.8b	(* (/ 1 (* (cbrt t) (cbrt t))) (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt t)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
53×	`add-exp-log`
51×	`times-frac`
40×	`*-un-lft-identity`
37×	`add-cube-cbrt`
27×	`cbrt-prod`
25×	`associate-r`
21×	`prod-exp` `add-cbrt-cube`
16×	`div-exp`
10×	`associate-l` `unswap-sqr`
9×	`cbrt-unprod`
8×	`pow1` `cbrt-undiv`
6×	`associate-/r*`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`associate-r/` `div-inv` `associate-/l`
2×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/`
1×	`distribute-rgt-in` `frac-times` `frac-2neg` `distribute-lft-in` `pow1/3` `associate-*l/` `clear-num`

Counts

4 → 144

Calls

4 calls:

1.0ms	(cbrt t)
33.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt t))
25.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
69.0ms	(* (/ 1 (* (cbrt t) (cbrt t))) (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt t)))

series693.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt t)
219.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt t))
90.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
197.0ms	(* (/ 1 (* (cbrt t) (cbrt t))) (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt t)))

simplify109.0ms

Counts

156 → 156

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	768	2292
1	4082	1976
2	5001	1883
done	5001	1883

prune518.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.3b

regimes710.0ms

Accuracy

74.8% (4.0b remaining)

Error of 8.3b against oracle of 4.3b and baseline of 20.2b

bsearch155.0ms

Steps

Iters	Range		Point
7	1.2449861131513245e-115	3.07325320309632e-113	1.8264381599139905e-113
10	-0.7465447619262514	-3.2626108287873416e-11	-5.050049854843211e-06

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	32
1	56	32
done	56	32

end0.0ms

sample3.1s

Algorithm

intervals

Results

730.0ms	1554×	body	10240	exit
710.0ms	1396×	body	1280	valid
441.0ms	1574×	body	640	valid
207.0ms	3579×	body	80	valid
157.0ms	932×	body	320	valid
96.0ms	77×	body	2560	valid
80.0ms	2466×	body	80	nan
52.0ms	469×	body	160	valid
48.0ms	263×	body	640	nan
28.0ms	106×	body	1280	nan
19.0ms	159×	body	320	nan
8.0ms	100×	body	160	nan