Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample26.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify90.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4970	14
1	4970	14

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 2

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 4.0 (sqrt x)))
0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.1b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
41×	`times-frac`
26×	`add-cube-cbrt` `associate-r`
12×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/l*`
4×	`flip3-+` `associate-/r*` `sum-log` `associate-/r/` `flip-+`
3×	`associate-l`
2×	`cbrt-undiv` `+-commutative` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`associate-+r+` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

4 → 116

Calls

4 calls:

3.0ms	(+ 1.0 (* 4.0 (sqrt x)))
7.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
13.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series23.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ 1.0 (* 4.0 (sqrt x)))
4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
8.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
7.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

simplify33.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5095	2111

prune189.0ms

Filtered

94 candidates to 128 candidates (-36.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	125	5	130

Merged error: 0b

Counts

130 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 6.0 (cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)))
0.1b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
0.1b	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))
0.1b	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

210×	`*-un-lft-identity`
153×	`add-sqr-sqrt`
142×	`times-frac`
122×	`cbrt-prod`
80×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
61×	`associate-r`
36×	`distribute-lft-out`
29×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r/`
11×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`pow1` `flip3-+` `flip-+` `div-inv` `unswap-sqr`
5×	`associate-/l*`
4×	`associate-/r*` `add-log-exp` `sqr-pow`
3×	`cube-div` `cube-mult` `pow-unpow` `unpow3` `associate-l`
2×	`cbrt-undiv` `cbrt-div` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 269

Calls

4 calls:

27.0ms	(* 6.0 (cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
12.0ms	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))
11.0ms	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)

series47.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* 6.0 (cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)))
7.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
11.0ms	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))
11.0ms	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)

simplify65.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5308	5747

prune304.0ms

Filtered

129 candidates to 281 candidates (-117.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	281	5	286

Merged error: 0b

Counts

286 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 6.0 (* (/ 1 (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))) (/ (- x 1.0) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
0.2b	(/ 1 (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.2b	(* (/ 1 (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))) (/ (- x 1.0) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
0.3b	(/ (- x 1.0) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x))))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

149×	`add-sqr-sqrt`
145×	`*-un-lft-identity`
134×	`times-frac`
83×	`sqrt-prod`
73×	`add-cube-cbrt`
64×	`add-exp-log`
42×	`associate-r`
38×	`add-cbrt-cube`
30×	`associate-l`
25×	`prod-exp`
19×	`div-exp`
18×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
14×	`associate-/r*`
13×	`pow1` `cbrt-unprod`
10×	`cbrt-undiv`
8×	`sqrt-div` `associate-/r/` `associate-/l*`
5×	`rec-exp` `1-exp` `associate-*r/`
4×	`flip3-+` `pow-prod-down` `flip-+` `div-inv` `add-log-exp`
3×	`pow-flip`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative` `associate-/l/`
1×	`flip3--` `sqrt-pow1` `pow1/2` `div-sub` `flip--` `inv-pow`

Counts

4 → 253

Calls

4 calls:

24.0ms	(* 6.0 (* (/ 1 (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))) (/ (- x 1.0) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
7.0ms	(/ 1 (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x))))))
35.0ms	(* (/ 1 (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))) (/ (- x 1.0) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
9.0ms	(/ (- x 1.0) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x))))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* 6.0 (* (/ 1 (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))) (/ (- x 1.0) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
10.0ms	(/ 1 (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x))))))
7.0ms	(* (/ 1 (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))) (/ (- x 1.0) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
15.0ms	(/ (- x 1.0) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4966	5886
1	4966	5886

prune438.0ms

Filtered

139 candidates to 265 candidates (-90.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	265	5	270

Merged error: 0b

Counts

270 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (- x 1.0))
0.3b	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
9×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `associate-r`
4×	`associate-*r/`
3×	`times-frac` `associate-l` `associate-/r*` `sum-log`
2×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 62

Calls

3 calls:

5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
6.0ms	(* 6.0 (- x 1.0))
10.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series15.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
3.0ms	(* 6.0 (- x 1.0))
8.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4992	903
1	4992	903

prune85.0ms

Filtered

54 candidates to 71 candidates (-31.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	71	5	76

Merged error: 0b

Counts

76 → 5

regimes71.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	17
1	28	17

end0.0ms

sample390.0ms

Algorithm

intervals

Results

304.0ms	8000×	body	80	valid
0.0ms	7×	body	80	nan

Details

analyze4.0ms

sample26.0ms

simplify90.0ms

prune7.0ms

localize8.0ms

rewrite36.0ms

series23.0ms

simplify33.0ms

prune189.0ms

localize11.0ms

rewrite73.0ms

series47.0ms

simplify65.0ms

prune304.0ms

localize14.0ms

rewrite88.0ms

series42.0ms

simplify97.0ms

prune438.0ms

localize9.0ms

rewrite23.0ms

series15.0ms

simplify39.0ms

prune85.0ms

regimes71.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample390.0ms

Profiling