Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	195×	body	80	valid
2.0ms	22×	body	640	valid
2.0ms	15×	body	1280	valid
1.0ms	15×	body	320	valid
0.0ms	9×	body	160	valid

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 22.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
3.3b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
7.8b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite68.0ms

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:

21.0ms	(* (- 1.0 x) y)
21.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
24.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series129.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* (- 1.0 x) y)
62.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
39.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (12.0ms)

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

prune135.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.2b	(/ (* (- 1.0 x) y) (sqrt (+ y 1.0)))
2.4b	(/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0)))
5.0b	(- 1.0 (/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 201

Calls

4 calls:

24.0ms	(* (- 1.0 x) y)
24.0ms	(/ (* (- 1.0 x) y) (sqrt (+ y 1.0)))
41.0ms	(/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0)))
63.0ms	(- 1.0 (/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0))))

series229.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- 1.0 x) y)
98.0ms	(/ (* (- 1.0 x) y) (sqrt (+ y 1.0)))
40.0ms	(/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0)))
64.0ms	(- 1.0 (/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0))))

simplify106.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	715	2414
1	3277	2119
2	5003	2107

prune350.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
0.0b	(- (/ 1 y) (/ x y))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`times-frac`
6×	`add-log-exp` `difference-of-squares`
5×	`div-inv` `distribute-lft-out--`
4×	`add-cube-cbrt` `associate-+l+`
3×	`sub-neg` `distribute-rgt-out--`
2×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
1×	`+-commutative` `flip3--` `flip3-+` `diff-log` `sum-log` `frac-sub` `flip--` `flip-+` `sub-div`

Counts

2 → 43

Calls

2 calls:

31.0ms	(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
29.0ms	(- (/ 1 y) (/ x y))

series47.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
18.0ms	(- (/ 1 y) (/ x y))

simplify89.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	224	317
1	627	291
2	2889	282
3	5001	274

prune77.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series681.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt y)
172.0ms	(cbrt y)
168.0ms	(cbrt y)
172.0ms	(cbrt y)

simplify135.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	40	156
1	81	144
2	193	136
3	696	136
4	4103	136
5	5002	136

prune143.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes185.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 27.3b

bsearch79.0ms

Steps

Iters	Range		Point
10	8.950540206577903e-05	1607394699600770.5	77921780.70844802
9	-1500.694570789724	-6.027254205251813e-06	-0.9906112633587307

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	31	14

end0.0ms

sample466.0ms

Algorithm

intervals

Results

153.0ms	6071×	body	80	valid
60.0ms	707×	body	640	valid
40.0ms	378×	body	1280	valid
34.0ms	545×	body	320	valid
13.0ms	299×	body	160	valid