Details

sample26.0ms

Algorithm

intervals

Results

9.0ms	187×	body	80	valid
4.0ms	26×	body	640	valid
3.0ms	16×	body	1280	valid
2.0ms	16×	body	320	valid
1.0ms	11×	body	160	valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	74	5
3	128	5
4	252	5
5	374	5
6	514	5
7	642	5
8	777	5
9	1010	5
10	1686	5
11	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.6b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.8b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

10.0ms	(* (- 1.0 x) y)
13.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series138.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* (- 1.0 x) y)
67.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
43.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	338	401
1	1456	359
2	5001	359

prune143.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
2.6b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 88

Calls

3 calls:

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

series145.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ y (+ y 1.0))
45.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
65.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	400	572
1	1790	526
2	5002	526

prune178.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) (* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0)))
0.1b	(* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0))
5.5b	(- 1.0 (* (- 1.0 x) (* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0))))
13.9b	(/ y (- (* y y) (* 1.0 1.0)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 147

Calls

4 calls:

32.0ms	(* (- 1.0 x) (* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0)))
27.0ms	(* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0))
4.0ms	(- 1.0 (* (- 1.0 x) (* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0))))
5.0ms	(/ y (- (* y y) (* 1.0 1.0)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (- 1.0 x) (* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0)))
59.0ms	(* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0))
157.0ms	(- 1.0 (* (- 1.0 x) (* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0))))
70.0ms	(/ y (- (* y y) (* 1.0 1.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	721	1566
1	3724	1431
2	5001	1429

prune332.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

4.3b	(* (* y (/ y (- (* y y) (* 1.0 1.0)))) (- 1.0 x))
5.1b	(- 1.0 (* (* y (/ y (- (* y y) (* 1.0 1.0)))) (- 1.0 x)))
13.9b	(/ y (- (* y y) (* 1.0 1.0)))
13.9b	(/ y (- (* y y) (* 1.0 1.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

25.0ms	(* (* y (/ y (- (* y y) (* 1.0 1.0)))) (- 1.0 x))
2.0ms	(- 1.0 (* (* y (/ y (- (* y y) (* 1.0 1.0)))) (- 1.0 x)))
5.0ms	(/ y (- (* y y) (* 1.0 1.0)))
5.0ms	(/ y (- (* y y) (* 1.0 1.0)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (* y (/ y (- (* y y) (* 1.0 1.0)))) (- 1.0 x))
103.0ms	(- 1.0 (* (* y (/ y (- (* y y) (* 1.0 1.0)))) (- 1.0 x)))
68.0ms	(/ y (- (* y y) (* 1.0 1.0)))
70.0ms	(/ y (- (* y y) (* 1.0 1.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	488	1093
1	2440	994
2	5002	988

prune313.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes111.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 22.9b

bsearch102.0ms

Steps

Iters	Range		Point
10	0.24914757354793585	7734910176.923709	239862300.49767068
9	-8.085901714425178e+20	-897362988193.2484	-913328192986.9236

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	14
1	33	14

end0.0ms

sample699.0ms

Algorithm

intervals

Results

300.0ms	6050×	body	80	valid
95.0ms	671×	body	640	valid
73.0ms	398×	body	1280	valid
62.0ms	553×	body	320	valid
28.0ms	328×	body	160	valid