Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
8.0ms	245×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	39	7
2	61	7
3	80	7
4	105	7
5	114	7
6	114	7

prune2.0ms

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: 0.1b

Counts

2 → 1

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

rewrite22.0ms

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` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l+` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 64

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))))

series18.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify53.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	492	549
1	2177	479
2	5002	478

prune105.0ms

Filtered

55 candidates to 73 candidates (-32.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Merged error: 0b

Counts

74 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `sum-log`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l+`

Counts

3 → 154

Calls

3 calls:

9.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
11.0ms	(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

series22.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
12.0ms	(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	822	2172
1	3767	2075
2	5001	2075

prune281.0ms

Filtered

129 candidates to 163 candidates (-26.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	163	4	167

Merged error: 0b

Counts

167 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
6.0ms	(* 6.0 (- x 1.0))
11.0ms	(/ 1 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (* 6.0 (- x 1.0))))
10.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (* 6.0 (- x 1.0)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
3.0ms	(* 6.0 (- x 1.0))
8.0ms	(/ 1 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (* 6.0 (- x 1.0))))
7.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (* 6.0 (- x 1.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	752	1425
1	3532	1257
2	5001	1209

prune142.0ms

Filtered

85 candidates to 140 candidates (-64.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	140	4	144

Merged error: 0b

Counts

144 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
0.1b	(* (* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
0.2b	(* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
14.3b	(/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

4.0ms	(+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
14.0ms	(* (* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
11.0ms	(* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
8.0ms	(/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

series24.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
10.0ms	(* (* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
4.0ms	(* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
7.0ms	(/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

simplify97.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	753	2109
1	3428	1853
2	5001	1834

prune244.0ms

Filtered

101 candidates to 136 candidates (-34.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	136	4	140

Merged error: 0b

Counts

140 → 4

regimes30.0ms

Accuracy

0% (0.0b 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 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

end0.0ms

sample808.0ms

Algorithm

intervals

Results

308.0ms	8000×	body	80	valid
271.0ms	7963×	body	80	nan

Details

sample27.0ms

simplify11.0ms

prune2.0ms

localize8.0ms

rewrite22.0ms

series18.0ms

simplify53.0ms

prune105.0ms

localize8.0ms

rewrite32.0ms

series22.0ms

simplify102.0ms

prune281.0ms

localize9.0ms

rewrite38.0ms

series22.0ms

simplify84.0ms

prune142.0ms

localize14.0ms

rewrite41.0ms

series24.0ms

simplify97.0ms

prune244.0ms

regimes30.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample808.0ms

Profiling