Details

sample522.0ms

Algorithm

intervals

Results

187.0ms	56×	body	2560	valid
62.0ms	90×	body	1280	valid
13.0ms	51×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	10×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (tan x))
1.2b	(- x (sin x))

rewrite22.0ms

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:

9.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series185.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- x (sin x)) (- x (tan x)))
54.0ms	(- x (tan x))
52.0ms	(- x (sin x))

simplify156.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune212.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
1.1b	(- x (tan x))
1.2b	(- x (sin x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
62×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 188

Calls

4 calls:

11.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
12.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
6.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series262.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
80.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
55.0ms	(- x (tan x))
32.0ms	(- x (sin x))

simplify79.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	736	2195
1	3051	2083
2	5001	2069

prune313.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.3b	(* 27/2800 (pow x 4))
14.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite24.0ms

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:

5.0ms	(* 9/40 (pow x 2))
5.0ms	(* 27/2800 (pow x 4))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series112.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 9/40 (pow x 2))
42.0ms	(* 27/2800 (pow x 4))
46.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5002	315

prune149.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin x) 3)
1.1b	(- x (tan x))
1.2b	(- (pow x 3) (pow (sin x) 3))
19.7b	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
49×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
16×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`frac-times`
3×	`difference-cubes` `pow-unpow` `flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-cube-cbrt`

Counts

4 → 147

Calls

4 calls:

3.0ms	(pow (sin x) 3)
4.0ms	(- x (tan x))
12.0ms	(- (pow x 3) (pow (sin x) 3))
28.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (sin x) 3)
50.0ms	(- x (tan x))
110.0ms	(- (pow x 3) (pow (sin x) 3))
253.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

simplify92.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	630	1900
1	3022	1778
2	5002	1734

prune411.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes74.0ms

Accuracy

100% (0.0b remaining)

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

bsearch83.0ms

Steps

Iters	Range		Point
10	1.4316099847845607e-10	21.660028671588154	0.02927114404593424
9	-8.718619127186496	-1.4100946153605287e-08	-0.02800886827920761

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.8s	1584×	body	2560	valid
1.6s	2769×	body	1280	valid
480.0ms	1889×	body	640	valid
153.0ms	913×	body	320	valid
61.0ms	487×	body	160	valid
26.0ms	358×	body	80	valid