Details

analyze3.0ms

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

sample16.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4935	14
1	4935	14

prune9.0ms

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 3 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 105

Calls

3 calls:

5.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
16.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series19.0ms

Counts

3 → 9

Calls

3 calls:

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)))))

simplify37.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5363	1958

prune188.0ms

Filtered

82 candidates to 114 candidates (-39.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	111	5	116

Merged error: 0b

Counts

116 → 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)))
0.0b	(/ (- 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)

rewrite69.0ms

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:

25.0ms	(* 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)))))
11.0ms	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))
10.0ms	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)

series45.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* 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)))))
10.0ms	(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)

simplify89.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5118	5747

prune416.0ms

Filtered

132 candidates to 281 candidates (-112.9%)

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 3 expressions with local error:

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

rewrite42.0ms

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:

13.0ms	(* 6.0 (- x 1.0))
9.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
18.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series24.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify30.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5171	920

prune107.0ms

Filtered

55 candidates to 71 candidates (-29.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	72	4	76

Merged error: 0b

Counts

76 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.1b	(/ (* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0))) (+ (+ x 1.0) (* 4.0 (sqrt x))))
0.1b	(* 6.0 (+ (sqrt x) (sqrt 1.0)))
0.2b	(* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

10.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
34.0ms	(/ (* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0))) (+ (+ x 1.0) (* 4.0 (sqrt x))))
8.0ms	(* 6.0 (+ (sqrt x) (sqrt 1.0)))
14.0ms	(* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
56.0ms	(/ (* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0))) (+ (+ x 1.0) (* 4.0 (sqrt x))))
8.0ms	(* 6.0 (+ (sqrt x) (sqrt 1.0)))
21.0ms	(* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0)))

simplify38.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4998	1948
1	4998	1948

prune233.0ms

Filtered

91 candidates to 116 candidates (-27.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	116	4	120

Merged error: 0b

Counts

120 → 4

regimes71.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	17
1	67	17

end0.0ms

sample417.0ms

Algorithm

intervals

Results

324.0ms	8000×	body	80	valid
0.0ms	1×	body	80	nan

Details

analyze3.0ms

sample16.0ms

simplify38.0ms

prune9.0ms

localize8.0ms

rewrite32.0ms

series19.0ms

simplify37.0ms

prune188.0ms

localize11.0ms

rewrite69.0ms

series45.0ms

simplify89.0ms

prune416.0ms

localize14.0ms

rewrite42.0ms

series24.0ms

simplify30.0ms

prune107.0ms

localize11.0ms

rewrite72.0ms

series95.0ms

simplify38.0ms

prune233.0ms

regimes71.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample417.0ms

Profiling