Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	68×	body	640	valid
5.0ms	129×	body	80	valid
3.0ms	16×	body	1280	valid
3.0ms	26×	body	320	valid
1.0ms	17×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	81	15
1	81	15

prune4.0ms

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: 8.9b

Counts

2 → 1

localize13.0ms

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))
2.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite59.0ms

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` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
16.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
29.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series20.0ms

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))
12.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4934	1608
1	4934	1608

prune188.0ms

Filtered

95 candidates to 126 candidates (-32.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	3	127

Merged error: 0.1b

Counts

127 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))
0.2b	(* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0))
5.7b	(+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)
12.2b	(/ (* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)) (* (- x 1.0) (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

16.0ms	(+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))
45.0ms	(* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0))
23.0ms	(+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)
68.0ms	(/ (* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)) (* (- x 1.0) (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))
14.0ms	(* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0))
8.0ms	(+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)
15.0ms	(/ (* (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (+ (* (- x 1.0) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))) 1.0)) (* (- x 1.0) (+ (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5103	3275

prune295.0ms

Filtered

94 candidates to 119 candidates (-26.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0.0b

Counts

122 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (* x (- (* x x) (* 1.0 1.0))))
0.0b	(* x (- (* x x) (* 1.0 1.0)))
0.2b	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
19.5b	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

18.0ms	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (* x (- (* x x) (* 1.0 1.0))))
6.0ms	(* x (- (* x x) (* 1.0 1.0)))
3.0ms	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
11.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify50.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5332	3761

prune315.0ms

Filtered

97 candidates to 125 candidates (-28.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	125	4	129

Merged error: 0.0b

Counts

129 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ 1.0 x))
0.0b	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (- (pow x 3) (* x 1.0)))
0.2b	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
19.5b	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

74×	`associate-*r/`
32×	`frac-add`
26×	`flip3--` `flip--`
19×	`flip3-+` `flip-+`
18×	`associate-/l/`
17×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`frac-times`
15×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-exp-log` `associate-*l/` `add-cbrt-cube` `add-log-exp`
7×	`distribute-rgt-in` `distribute-lft-in`
6×	`pow1`
4×	`cube-mult` `associate-+l+` `associate-+r+` `associate-r` `associate-/r*` `distribute-lft-out--`
3×	`sub-neg` `associate-l` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 121

Calls

4 calls:

8.0ms	(* x (+ 1.0 x))
17.0ms	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (- (pow x 3) (* x 1.0)))
3.0ms	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
11.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

series15.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* x (+ 1.0 x))
5.0ms	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (- (pow x 3) (* x 1.0)))
3.0ms	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
1.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

simplify63.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5007	4164

prune383.0ms

Filtered

110 candidates to 133 candidates (-20.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	133	4	137

Merged error: 0.0b

Counts

137 → 4

regimes60.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 28.7b

bsearch34.0ms

Steps

Iters	Range		Point
10	0.009091900342010817	66730311810763.45	169090.9027696541
7	-5486.906575454437	-60.40944958396893	-4144.93602321544

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	95
1	57	95

end0.0ms

sample847.0ms

Algorithm

intervals

Results

284.0ms	1846×	body	640	valid
168.0ms	4172×	body	80	valid
114.0ms	571×	body	1280	valid
106.0ms	907×	body	320	valid
39.0ms	507×	body	160	valid

Details

sample29.0ms

simplify4.0ms

prune4.0ms

localize13.0ms

rewrite59.0ms

series20.0ms

simplify67.0ms

prune188.0ms

localize16.0ms

rewrite156.0ms

series40.0ms

simplify52.0ms

prune295.0ms

localize19.0ms

rewrite44.0ms

series17.0ms

simplify50.0ms

prune315.0ms

localize16.0ms

rewrite45.0ms

series15.0ms

simplify63.0ms

prune383.0ms

regimes60.0ms

bsearch34.0ms

simplify1.0ms

end0.0ms

sample847.0ms

Profiling