Details

sample446.0ms

Algorithm

intervals

Results

99.0ms	47×	body	2560	valid
63.0ms	89×	body	1280	valid
24.0ms	66×	body	640	valid
8.0ms	31×	body	320	valid
3.0ms	15×	body	160	valid
1.0ms	8×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (sin x))
1.4b	(- 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))
6.0ms	(- x (tan x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
61.0ms	(- 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

prune210.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

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)))
1.4b	(- x (sin x))
1.4b	(- x (tan x))

rewrite43.0ms

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)))))
11.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
2.0ms	(- x (tan x))

series234.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(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))

simplify41.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (9.0ms)

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

prune329.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (cos x) 2)
14.5b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
14.6b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
42×	`div-exp`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
14×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow-pow` `frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 136

Calls

4 calls:

1.0ms	(pow (sin x) 2)
1.0ms	(pow (cos x) 2)
8.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
7.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin x) 2)
17.0ms	(pow (cos x) 2)
72.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
60.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	410	1022
1	1776	914
2	5001	914

prune346.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 9/40 (pow x 2))
0.3b	(* 27/2800 (pow x 4))
15.8b	(- (* 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:

6.0ms	(* 9/40 (pow x 2))
5.0ms	(* 27/2800 (pow x 4))
8.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series112.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(* 9/40 (pow x 2))
35.0ms	(* 27/2800 (pow x 4))
47.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify43.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (37.0ms)

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

prune142.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes53.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch109.0ms

Steps

Iters	Range		Point
10	4.8244160186105205e-08	257763.20554958374	0.029859806300954833
10	-772.3369502403921	-4.163765984402517e-10	-0.026495654945468235

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	13
1	31	13

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.5s	1592×	body	2560	valid
2.0s	2794×	body	1280	valid
688.0ms	1883×	body	640	valid
236.0ms	956×	body	320	valid
77.0ms	440×	body	160	valid
52.0ms	335×	body	80	valid