Details

sample464.0ms

Algorithm

intervals

Results

101.0ms	46×	body	2560	valid
70.0ms	95×	body	1280	valid
26.0ms	65×	body	640	valid
9.0ms	33×	body	320	valid
2.0ms	8×	body	160	valid
1.0ms	9×	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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.5b	(- x (sin x))
1.5b	(- x (tan x))

rewrite24.0ms

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:

12.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series177.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
31.0ms	(- x (sin x))
69.0ms	(- x (tan x))

simplify149.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

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

prune223.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
16.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite22.0ms

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:

6.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
8.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series111.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 9/40 (pow x 2))
50.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify47.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315

prune155.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

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))
1.5b	(- x (sin x))
1.5b	(- x (tan x))

rewrite48.0ms

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:

14.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
18.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
3.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series261.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
80.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
37.0ms	(- x (sin x))
50.0ms	(- x (tan x))

simplify78.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (59.0ms)

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

prune322.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.5b	(- x (tan x))
1.5b	(- x (tan x))
1.5b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite72.0ms

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:

7.0ms	(/ (sin x) (- x (tan x)))
3.0ms	(- x (tan x))
2.0ms	(- x (tan x))
56.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (sin x) (- x (tan x)))
56.0ms	(- x (tan x))
56.0ms	(- x (tan x))
180.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

simplify44.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	872
2	5001	872

prune259.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes51.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.0b

bsearch109.0ms

Steps

Iters	Range		Point
9	2.0114125408603258e-10	0.4954286465087044	0.024314219703607573
10	-1.7081313977704333	-1.7977825652338532e-10	-0.032009009980635265

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	21
1	32	21

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.8s	1630×	body	2560	valid
2.1s	2795×	body	1280	valid
728.0ms	1823×	body	640	valid
239.0ms	905×	body	320	valid
91.0ms	474×	body	160	valid
53.0ms	373×	body	80	valid