Details

analyze6.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample30.0ms

Algorithm

intervals

Results

9.0ms	66×	body	640	valid
8.0ms	138×	body	80	valid
3.0ms	17×	body	1280	valid
3.0ms	24×	body	320	valid
1.0ms	11×	body	160	valid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	880	15
1	880	15

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 9.2b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+l+`

Counts

4 → 112

Calls

4 calls:

8.0ms	(/ 1.0 (- x 1.0))
8.0ms	(/ 1.0 (+ x 1.0))
18.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
29.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1.0 (- x 1.0))
2.0ms	(/ 1.0 (+ x 1.0))
3.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
18.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4949	1594
1	4949	1594

prune217.0ms

Filtered

95 candidates to 124 candidates (-30.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	3	125

Merged error: 0.3b

Counts

125 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ 1.0 (+ 1.0 x)))
0.0b	(sqrt (/ 1.0 (+ 1.0 x)))
0.1b	(* (sqrt (/ 1.0 (+ 1.0 x))) (sqrt (/ 1.0 (+ 1.0 x))))
5.8b	(+ (- (* (sqrt (/ 1.0 (+ 1.0 x))) (sqrt (/ 1.0 (+ 1.0 x)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

134×	`sqrt-prod`
116×	`*-un-lft-identity`
94×	`add-sqr-sqrt`
92×	`times-frac`
60×	`add-cube-cbrt`
29×	`swap-sqr`
25×	`distribute-lft-out`
21×	`pow1` `associate-r` `associate-l`
12×	`associate-/r/`
10×	`sqrt-pow1` `pow1/2` `sqrt-div`
9×	`add-log-exp` `unswap-sqr`
7×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `div-inv`
5×	`frac-add` `pow-prod-up`
4×	`rem-sqrt-square`
3×	`pow-prod-down` `pow-sqr` `frac-sub`
2×	`frac-times` `associate-r/` `associate-l/` `sum-log`
1×	`+-commutative` `pow2` `associate-+l-` `sub-neg` `associate-+l+` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 188

Calls

4 calls:

5.0ms	(sqrt (/ 1.0 (+ 1.0 x)))
5.0ms	(sqrt (/ 1.0 (+ 1.0 x)))
20.0ms	(* (sqrt (/ 1.0 (+ 1.0 x))) (sqrt (/ 1.0 (+ 1.0 x))))
25.0ms	(+ (- (* (sqrt (/ 1.0 (+ 1.0 x))) (sqrt (/ 1.0 (+ 1.0 x)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (/ 1.0 (+ 1.0 x)))
7.0ms	(sqrt (/ 1.0 (+ 1.0 x)))
6.0ms	(* (sqrt (/ 1.0 (+ 1.0 x))) (sqrt (/ 1.0 (+ 1.0 x))))
9.0ms	(+ (- (* (sqrt (/ 1.0 (+ 1.0 x))) (sqrt (/ 1.0 (+ 1.0 x)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4939	2700
1	4939	2700

prune389.0ms

Filtered

130 candidates to 200 candidates (-53.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	200	3	203

Merged error: 0.3b

Counts

203 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0)))
0.0b	(* x (+ 1.0 x))
0.1b	(* x (- (* x x) (* 1.0 1.0)))
16.0b	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

42×	`associate-*r/`
19×	`flip3--` `flip--`
18×	`add-sqr-sqrt`
16×	`frac-add`
14×	`*-un-lft-identity`
12×	`frac-times`
11×	`associate-r` `associate-l`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `flip3-+` `add-cbrt-cube` `flip-+`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`sub-neg` `associate-*l/` `add-log-exp`
4×	`associate-+r+`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-+l+` `difference-of-squares`
1×	`+-commutative` `sum-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 109

Calls

4 calls:

9.0ms	(* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0)))
6.0ms	(* x (+ 1.0 x))
6.0ms	(* x (- (* x x) (* 1.0 1.0)))
12.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

series18.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0)))
4.0ms	(* x (+ 1.0 x))
7.0ms	(* x (- (* x x) (* 1.0 1.0)))
1.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

simplify42.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5650	2807

prune286.0ms

Filtered

96 candidates to 121 candidates (-26.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	121	3	124

Merged error: 0.3b

Counts

124 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ 1.0 x))
0.0b	(* x (- (pow x 4) (pow 1.0 4)))
16.0b	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))
17.7b	(/ (* x (- (pow x 4) (pow 1.0 4))) (+ (* x x) (* 1.0 1.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

6.0ms	(* x (+ 1.0 x))
11.0ms	(* x (- (pow x 4) (pow 1.0 4)))
12.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))
13.0ms	(/ (* x (- (pow x 4) (pow 1.0 4))) (+ (* x x) (* 1.0 1.0)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* x (+ 1.0 x))
10.0ms	(* x (- (pow x 4) (pow 1.0 4)))
1.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))
14.0ms	(/ (* x (- (pow x 4) (pow 1.0 4))) (+ (* x x) (* 1.0 1.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5054	2680

prune370.0ms

Filtered

101 candidates to 126 candidates (-24.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	126	3	129

Merged error: 0.3b

Counts

129 → 3

regimes41.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 20.1b

bsearch35.0ms

Steps

Iters	Range		Point
9	440.4259595560071	243476276.19758523	569.3349891167142
8	-388617481261202.44	-177468938200.04388	-370328111107034.1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	116	45
1	116	45

end0.0ms

sample769.0ms

Algorithm

intervals

Results

261.0ms	1843×	body	640	valid
161.0ms	4117×	body	80	valid
113.0ms	625×	body	1280	valid
104.0ms	973×	body	320	valid
32.0ms	442×	body	160	valid
0.0ms	3×	body	80	invalid

Details

analyze6.0ms

sample30.0ms

simplify47.0ms

prune5.0ms

localize8.0ms

rewrite71.0ms

series25.0ms

simplify47.0ms

prune217.0ms

localize11.0ms

rewrite66.0ms

series29.0ms

simplify70.0ms

prune389.0ms

localize16.0ms

rewrite36.0ms

series18.0ms

simplify42.0ms

prune286.0ms

localize22.0ms

rewrite48.0ms

series29.0ms

simplify81.0ms

prune370.0ms

regimes41.0ms

bsearch35.0ms

simplify2.0ms

end0.0ms

sample769.0ms

Profiling