Details

sample485.0ms

Algorithm

intervals

Results

142.0ms	50×	body	2560	valid
64.0ms	95×	body	1280	valid
17.0ms	54×	body	640	valid
7.0ms	33×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	12×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

14.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series175.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854

prune243.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`associate-/r` `associate-/l`
4×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `expm1-log1p` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv` `expm1-udef`

Counts

4 → 121

Calls

4 calls:

0.0ms	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
13.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series283.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
74.0ms	(/ (- x (sin x)) (- x (tan x)))
48.0ms	(- x (tan x))
34.0ms	(- x (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	484	1189
1	1751	973
2	5001	973

prune307.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (* (- x (sin x)) (/ 1 (- x (tan x))))))
0.1b	(* (- x (sin x)) (/ 1 (- x (tan x))))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
28×	`add-cube-cbrt`
21×	`associate-r`
18×	`prod-diff`
17×	`times-frac`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-neg` `distribute-lft-out--` `difference-of-squares`
5×	`flip3--` `associate-l` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `diff-log` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `expm1-log1p` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `expm1-udef`

Counts

4 → 119

Calls

4 calls:

0.0ms	(expm1 (log1p (* (- x (sin x)) (/ 1 (- x (tan x))))))
26.0ms	(* (- x (sin x)) (/ 1 (- x (tan x))))
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series285.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(expm1 (log1p (* (- x (sin x)) (/ 1 (- x (tan x))))))
76.0ms	(* (- x (sin x)) (/ 1 (- x (tan x))))
48.0ms	(- x (tan x))
34.0ms	(- x (sin x))

simplify64.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	527	1107
1	2236	856
2	5002	836

prune307.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
0.1b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
64×	`add-cube-cbrt`
62×	`unpow-prod-down` `cube-prod`
42×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `fma-neg` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 220

Calls

4 calls:

15.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
16.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series256.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
93.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
55.0ms	(- x (tan x))
32.0ms	(- x (sin x))

simplify96.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	853	2547
1	3624	2257
2	5001	2239

prune416.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes39.0ms

Accuracy

100% (0.0b remaining)

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

bsearch88.0ms

Steps

Iters	Range		Point
9	0.0002199982819353488	137964.03928948785	0.02902705871059986
9	-0.41295360884021565	-1.1902930357079885e-07	-0.02453727723232867

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15

end0.0ms

sample7.0s

Algorithm

intervals

Results

4.2s	1645×	body	2560	valid
1.8s	2727×	body	1280	valid
577.0ms	1858×	body	640	valid
197.0ms	928×	body	320	valid
70.0ms	477×	body	160	valid
32.0ms	365×	body	80	valid