Details

sample483.0ms

Algorithm

intervals

Results

207.0ms	47×	body	2560	valid
88.0ms	87×	body	1280	valid
39.0ms	58×	body	640	valid
17.0ms	37×	body	320	valid
4.0ms	16×	body	160	valid
2.0ms	11×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (sin x))
1.1b	(- x (tan x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

25.0ms	(/ (- x (sin x)) (- x (tan x)))
12.0ms	(- x (sin x))
39.0ms	(- x (tan x))

series228.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(/ (- x (sin x)) (- x (tan x)))
38.0ms	(- x (sin x))
78.0ms	(- x (tan x))

simplify765.0ms

Counts

89 → 89

Iterations

Useful iterations: done (761.0ms)

Iter	Nodes	Cost
0	157	1237
1	371	1200
2	1360	1149
done	5000	1147

prune457.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.9b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.1b	(- x (tan x))
1.1b	(- x (tan x))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

17.0ms	(/ (sin x) (- x (tan x)))
141.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
8.0ms	(- x (tan x))
6.0ms	(- x (tan x))

series580.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (sin x) (- x (tan x)))
324.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
68.0ms	(- x (tan x))
101.0ms	(- x (tan x))

simplify786.0ms

Counts

106 → 106

Iterations

Useful iterations: done (783.0ms)

Iter	Nodes	Cost
0	177	1565
1	388	1511
2	1424	1450
done	5000	1449

prune483.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

1.1b	(- x (tan x))
1.1b	(- x (tan x))
1.1b	(- x (tan x))
1.1b	(- x (tan x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

11.0ms	(- x (tan x))
11.0ms	(- x (tan x))
12.0ms	(- x (tan x))
11.0ms	(- x (tan x))

series289.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- x (tan x))
69.0ms	(- x (tan x))
87.0ms	(- x (tan x))
63.0ms	(- x (tan x))

simplify1.3s

Counts

68 → 68

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	46	580
1	94	564
2	215	528
3	554	528
4	1701	528
done	5000	528

prune467.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b	(* 27/2800 (pow x 4))
0.4b	(* 9/40 (pow x 2))
13.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

24.0ms	(* 27/2800 (pow x 4))
12.0ms	(* 9/40 (pow x 2))
31.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series165.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* 27/2800 (pow x 4))
36.0ms	(* 9/40 (pow x 2))
58.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify918.0ms

Counts

75 → 75

Iterations

Useful iterations: done (916.0ms)

Iter	Nodes	Cost
0	121	788
1	291	703
2	1116	645
done	5000	643

prune278.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes64.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch199.0ms

Steps

Iters	Range		Point
11	9.093534403752284e-26	13730598.322931442	0.028184310562944685
8	-24.398001816905442	-0.001242952878385433	-0.02915223248619924

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	32	131
1	40	77
done	40	77

end0.0ms

sample13.9s

Algorithm

intervals

Results

6.6s	1592×	body	2560	valid
4.0s	2712×	body	1280	valid
1.9s	1928×	body	640	valid
640.0ms	945×	body	320	valid
186.0ms	455×	body	160	valid
132.0ms	368×	body	80	valid