Details

sample494.0ms

Algorithm

intervals

Results

224.0ms	47×	body	2560	valid
105.0ms	87×	body	1280	valid
50.0ms	58×	body	640	valid
17.0ms	37×	body	320	valid
4.0ms	16×	body	160	valid
2.0ms	11×	body	80	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize16.0ms

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))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

35.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (sin x))
41.0ms	(- x (tan x))

series222.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ (- x (sin x)) (- x (tan x)))
48.0ms	(- x (sin x))
86.0ms	(- x (tan x))

simplify1.8s

Counts

119 → 119

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	209	1823
1	501	1569
2	2264	1386
done	5002	1362

prune484.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 588

Calls

4 calls:

17.0ms	(/ (sin x) (- x (tan x)))
148.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
13.0ms	(- x (tan x))
14.0ms	(- x (tan x))

series515.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (sin x) (- x (tan x)))
281.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
82.0ms	(- x (tan x))
74.0ms	(- x (tan x))

simplify2.8s

Counts

600 → 600

Iterations

Useful iterations: 2 (907.0ms)

Iter	Nodes	Cost
0	617	35000
1	1404	31493
2	4797	24519
done	5000	24519

prune2.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

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))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

9.0ms	(- x (tan x))
7.0ms	(- x (tan x))
7.0ms	(- x (tan x))
7.0ms	(- x (tan x))

series263.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- x (tan x))
55.0ms	(- x (tan x))
76.0ms	(- x (tan x))
71.0ms	(- x (tan x))

simplify9.5s

Counts

124 → 124

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	73	1712
1	162	1264
2	582	968
3	4716	812
done	5000	812

prune647.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b	(fma 27/2800 (pow x 4) 1/2)
0.4b	(* 9/40 (pow x 2))
13.8b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 58

Calls

3 calls:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
26.0ms	(* 9/40 (pow x 2))
24.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series265.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(fma 27/2800 (pow x 4) 1/2)
51.0ms	(* 9/40 (pow x 2))
86.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify1.5s

Counts

67 → 67

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	106	845
1	250	714
2	1251	624
done	5001	581

prune280.0ms

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

bsearch178.0ms

Steps

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

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	30	128
1	36	75
done	36	75

end0.0ms

sample12.4s

Algorithm

intervals

Results

5.9s	1592×	body	2560	valid
4.1s	2712×	body	1280	valid
1.3s	1928×	body	640	valid
621.0ms	945×	body	320	valid
127.0ms	455×	body	160	valid
119.0ms	368×	body	80	valid