Details

sample254.0ms

Algorithm

intervals

Results

114.0ms	56×	body	2560	valid
85.0ms	79×	body	1280	valid
26.0ms	58×	body	640	valid
11.0ms	38×	body	320	valid
3.0ms	17×	body	160	valid
1.0ms	8×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
3	16
2	14
1	11
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

28.0ms	(/ (- 1.0 (cos x)) (sin x))
10.0ms	(- 1.0 (cos x))

series112.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (- 1.0 (cos x)) (sin x))
50.0ms	(- 1.0 (cos x))

simplify501.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	805
1	240
0	106

prune343.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ (* x (* x 1/24)) 1/2))
0.1b	(* 1/240 (pow x 5))
0.1b	(* x (* x 1/24))
0.4b	(* x 1/24)

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`associate-r`
13×	`pow1`
12×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
8×	`prod-exp`
6×	`cbrt-unprod`
5×	`pow-prod-down` `unswap-sqr`
4×	`unpow-prod-down` `*-commutative` `add-log-exp`
2×	`associate-*r/` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 83

Calls

4 calls:

78.0ms	(* x (+ (* x (* x 1/24)) 1/2))
17.0ms	(* 1/240 (pow x 5))
12.0ms	(* x (* x 1/24))
6.0ms	(* x 1/24)

series313.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* x (+ (* x (* x 1/24)) 1/2))
85.0ms	(* 1/240 (pow x 5))
42.0ms	(* x (* x 1/24))
29.0ms	(* x 1/24)

simplify879.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1637
1	358
0	130

prune449.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.5b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.1b	(- 1.0 (cos x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*`
3×	`log-prod` `associate-/r*` `div-sub` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

14.0ms	(/ (- 1.0 (cos x)) (sin x))
17.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
30.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
5.0ms	(- 1.0 (cos x))

series170.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
47.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
49.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
32.0ms	(- 1.0 (cos x))

simplify535.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	962
1	318
0	163

prune651.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (/ 1 (sin x)) (- 1.0 (cos x)))
2.1b	(- 1.0 (cos x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-l`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-r` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`associate-/r` `sub-neg` `flip3--` `flip--` `associate-/l` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `rec-exp` `distribute-lft-in` `1-exp` `associate-*r/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`clear-num` `frac-2neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 90

Calls

3 calls:

5.0ms	(/ 1 (sin x))
45.0ms	(* (/ 1 (sin x)) (- 1.0 (cos x)))
8.0ms	(- 1.0 (cos x))

series109.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ 1 (sin x))
53.0ms	(* (/ 1 (sin x)) (- 1.0 (cos x)))
26.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

99 → 99

Iterations

Iter	Nodes
done	5004
2	2400
1	380
0	150

prune287.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

regimes251.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 32.2b

bsearch133.0ms

Steps

Iters	Range		Point
10	5.09324609688744e-06	47495130.80298876	0.022350989698977898
10	-1138.2876542095912	-1.6260248627107784e-07	-0.01927343743819967

simplify10.0ms

Iterations

Iter	Nodes
done	48
1	48
0	39

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.3s	1579×	body	2560	valid
2.8s	2757×	body	1280	valid
1.1s	1907×	body	640	valid
792.0ms	945×	body	320	valid
97.0ms	323×	body	80	valid
94.0ms	487×	body	160	valid
18.0ms	2×	body	5120	valid