Details

sample465.0ms

Algorithm

intervals

Results

139.0ms	51×	body	2560	valid
50.0ms	91×	body	1280	valid
16.0ms	61×	body	640	valid
4.0ms	25×	body	320	valid
3.0ms	22×	body	160	valid
0.0ms	6×	body	80	valid

simplify12.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.9b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.6b	(- x (tan x))
2.7b	(- x (sin x))

rewrite37.0ms

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))

series184.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- x (sin x)) (- x (tan x)))
61.0ms	(- x (tan x))
43.0ms	(- x (sin x))

simplify148.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	360	718
1	1133	685
2	4726	685
3	5003	685

prune164.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	3	90

Merged error: 0.0b

Counts

90 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.4b	(* 9/40 (pow x 2))
14.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

6.0ms	(* 27/2800 (pow x 4))
7.0ms	(* 9/40 (pow x 2))
28.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series113.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 27/2800 (pow x 4))
28.0ms	(* 9/40 (pow x 2))
47.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	293	472
1	1125	437
2	5002	436

prune129.0ms

Filtered

89 candidates to 50 candidates (56.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	89	3	92

Merged error: 0.0b

Counts

92 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.5b	(* (pow x 2) (pow (cos x) 2))
15.5b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
15.8b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

456×	`times-frac`
425×	`add-sqr-sqrt`
356×	`unpow-prod-down`
213×	`*-un-lft-identity`
211×	`add-cube-cbrt`
196×	`unswap-sqr`
178×	`unpow2` `sqr-pow`
152×	`associate-l`
107×	`associate-r`
102×	`add-exp-log`
57×	`associate-/r*`
45×	`prod-exp`
42×	`pow-to-exp` `div-exp` `pow-exp`
19×	`*-commutative`
16×	`add-cbrt-cube` `associate-/l*`
11×	`pow-unpow`
9×	`pow1`
8×	`pow-prod-down`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-pow` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 671

Calls

4 calls:

2.0ms	(pow (cos x) 2)
11.0ms	(* (pow x 2) (pow (cos x) 2))
30.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
16.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (cos x) 2)
54.0ms	(* (pow x 2) (pow (cos x) 2))
77.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
65.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

simplify109.0ms

Algorithm

egg-herbie

Counts

683 → 683

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1640	7598
1	5002	6447

prune1.2s

Filtered

683 candidates to 275 candidates (40.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	683	0	683
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	683	3	686

Merged error: 0.0b

Counts

686 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin x) 3)
2.6b	(- (pow x 3) (pow (sin x) 3))
2.6b	(- x (tan x))
37.0b	(/ (- (pow x 3) (pow (sin x) 3)) (+ (* (sin x) (+ (sin x) x)) (pow x 2)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
117×	`add-sqr-sqrt`
90×	`times-frac`
64×	`difference-of-squares`
59×	`unpow-prod-down`
43×	`sqr-pow`
38×	`distribute-lft-out`
31×	`add-cube-cbrt` `pow-unpow`
28×	`difference-cubes`
19×	`associate-l`
18×	`associate-/l*`
15×	`distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
3×	`flip3--` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 190

Calls

4 calls:

2.0ms	(pow (sin x) 3)
9.0ms	(- (pow x 3) (pow (sin x) 3))
3.0ms	(- x (tan x))
31.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (+ (* (sin x) (+ (sin x) x)) (pow x 2)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (sin x) 3)
113.0ms	(- (pow x 3) (pow (sin x) 3))
51.0ms	(- x (tan x))
211.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (+ (* (sin x) (+ (sin x) x)) (pow x 2)))

simplify93.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	689	2939
1	2507	2861
2	5002	2853

prune355.0ms

Filtered

202 candidates to 100 candidates (49.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	202	3	205

Merged error: 0.0b

Counts

205 → 3

regimes33.0ms

Accuracy

99% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.2b

bsearch108.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	2.4056784657088475
10	-1556119314.230081	-0.05767290693153419	-2.4709346097908487

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	29
1	48	29

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.9s	1561×	body	2560	valid
1.7s	2812×	body	1280	valid
475.0ms	1822×	body	640	valid
156.0ms	936×	body	320	valid
58.0ms	485×	body	160	valid
28.0ms	384×	body	80	valid