Details

sample461.0ms

Algorithm

intervals

Results

104.0ms	51×	body	2560	valid
56.0ms	85×	body	1280	valid
22.0ms	62×	body	640	valid
8.0ms	36×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	6×	body	80	valid

simplify11.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite56.0ms

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:

36.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series168.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (- x (sin x)) (- x (tan x)))
54.0ms	(- x (tan x))
39.0ms	(- x (sin x))

simplify152.0ms

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

prune208.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 9/40 (pow x 2))
0.5b	(* 27/2800 (pow x 4))
16.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite44.0ms

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:

12.0ms	(* 9/40 (pow x 2))
11.0ms	(* 27/2800 (pow x 4))
18.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series107.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* 9/40 (pow x 2))
34.0ms	(* 27/2800 (pow x 4))
45.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify41.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

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

prune149.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 9/40 (pow x 2))
0.5b	(* 27/2800 (pow x 4))
16.1b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite39.0ms

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`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

12.0ms	(* 9/40 (pow x 2))
15.0ms	(* 27/2800 (pow x 4))
10.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series166.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 9/40 (pow x 2))
39.0ms	(* 27/2800 (pow x 4))
103.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify41.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	249	310
1	1003	281
2	5002	275

prune149.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 3)
1.7b	(- x (tan x))
1.7b	(- (pow x 3) (pow (sin x) 3))
20.4b	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

rewrite137.0ms

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:

4.0ms	(pow (sin x) 3)
5.0ms	(- x (tan x))
26.0ms	(- (pow x 3) (pow (sin x) 3))
94.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (sin x) 3)
52.0ms	(- x (tan x))
95.0ms	(- (pow x 3) (pow (sin x) 3))
241.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

simplify93.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (76.0ms)

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

prune420.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes52.0ms

Accuracy

100% (0.0b remaining)

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

bsearch85.0ms

Steps

Iters	Range		Point
10	8.950540206577903e-05	66689094922.78456	0.028137121054087433
10	-1500.694570789724	-6.177030851099824e-09	-0.029160662270036743

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	11
1	28	11

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.5s	1601×	body	2560	valid
1.8s	2790×	body	1280	valid
621.0ms	1874×	body	640	valid
206.0ms	930×	body	320	valid
71.0ms	474×	body	160	valid
37.0ms	331×	body	80	valid