Details

sample428.0ms

Algorithm

intervals

Results

86.0ms	43×	body	2560	valid
54.0ms	86×	body	1280	valid
24.0ms	69×	body	640	valid
5.0ms	23×	body	320	valid
3.0ms	20×	body	160	valid
1.0ms	15×	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: 31.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.0b	(- x (sin x))
2.3b	(- x (tan x))

rewrite35.0ms

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))

series175.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
62.0ms	(- x (tan 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

prune221.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
0.0b	(/ (- x (sin x)) (- x (tan x)))
2.0b	(- x (sin x))
2.3b	(- x (tan x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
32×	`log-pow`
31×	`exp-prod`
28×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 124

Calls

4 calls:

21.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
12.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series235.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
75.0ms	(/ (- x (sin x)) (- x (tan x)))
30.0ms	(- x (sin x))
53.0ms	(- x (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	430	1079
1	1247	1027
2	5001	1027

prune352.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.3b	(* 9/40 (pow x 2))
16.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite21.0ms

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	(* 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))

series109.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 27/2800 (pow x 4))
29.0ms	(* 9/40 (pow x 2))
44.0ms	(- (* 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	5001	315

prune160.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.3b	(* 9/40 (pow x 2))
16.8b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite16.0ms

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:

5.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
3.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series170.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 27/2800 (pow x 4))
29.0ms	(* 9/40 (pow x 2))
105.0ms	(- (* 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	5001	275

prune151.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes60.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.9b

bsearch87.0ms

Steps

Iters	Range		Point
10	4.555257425893614e-05	47183757994.54101	0.025407348733278587
9	-13600.963204601821	-0.00047371797307045637	-0.028226607772703794

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	13
1	30	13

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.3s	1547×	body	2560	valid
1.9s	2813×	body	1280	valid
679.0ms	1930×	body	640	valid
216.0ms	923×	body	320	valid
85.0ms	458×	body	160	valid
31.0ms	329×	body	80	valid