Details

sample51.0ms

Algorithm

intervals

Results

18.0ms	271×	body	80	valid
17.0ms	261×	body	80	nan

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	7
1	65	7
2	182	7
3	338	7
4	488	7
5	757	7
6	1166	7
7	1729	7
8	2793	7
9	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ 1.0 (* x 9.0)))
0.2b	(* 3.0 (sqrt x))
0.3b	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(/ 1.0 (* x 9.0))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

5.0ms	(+ y (/ 1.0 (* x 9.0)))
4.0ms	(* 3.0 (sqrt x))
71.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
3.0ms	(/ 1.0 (* x 9.0))

series147.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ y (/ 1.0 (* x 9.0)))
37.0ms	(* 3.0 (sqrt x))
67.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
17.0ms	(/ 1.0 (* x 9.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	456	548
1	2172	486
2	5002	484

prune189.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ 0.1111111111111111 x)) 1.0)
0.0b	(+ y (/ 0.1111111111111111 x))
0.2b	(* 3.0 (sqrt x))
0.3b	(* (* 3.0 (sqrt x)) (- (+ y (/ 0.1111111111111111 x)) 1.0))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

53.0ms	(- (+ y (/ 0.1111111111111111 x)) 1.0)
6.0ms	(+ y (/ 0.1111111111111111 x))
4.0ms	(* 3.0 (sqrt x))
89.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 0.1111111111111111 x)) 1.0))

series152.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(- (+ y (/ 0.1111111111111111 x)) 1.0)
25.0ms	(+ y (/ 0.1111111111111111 x))
36.0ms	(* 3.0 (sqrt x))
65.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 0.1111111111111111 x)) 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	398	528
1	1782	466
2	5001	464

prune172.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 (sqrt x)) (- (+ y (* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))) 1.0))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(/ 1.0 (* x 9.0))
0.5b	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
34×	`sqrt-prod`
24×	`pow1`
23×	`*-un-lft-identity`
21×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
18×	`times-frac`
15×	`associate-r`
12×	`swap-sqr`
11×	`associate-l`
8×	`sqrt-pow1` `pow1/2`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
5×	`pow-prod-up`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `pow-sqr`
2×	`sub-neg` `frac-2neg` `associate--l+` `clear-num` `associate-/r` `-commutative`
1×	`pow2` `frac-times` `flip3--` `pow-plus` `sqrt-unprod` `associate-*l/` `rem-square-sqrt` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 134

Calls

4 calls:

31.0ms	(* (* 3.0 (sqrt x)) (- (+ y (* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))) 1.0))
3.0ms	(/ 1.0 (* x 9.0))
3.0ms	(/ 1.0 (* x 9.0))
20.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

series236.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (* 3.0 (sqrt x)) (- (+ y (* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))) 1.0))
17.0ms	(/ 1.0 (* x 9.0))
16.0ms	(/ 1.0 (* x 9.0))
61.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

simplify80.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	512	957
1	2817	765
2	5002	722

prune318.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 (* x 9.0)) y)
0.1b	(* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(* (* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0)) (sqrt x))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

8.0ms	(+ (/ 1.0 (* x 9.0)) y)
110.0ms	(* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0))
3.0ms	(/ 1.0 (* x 9.0))
131.0ms	(* (* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0)) (sqrt x))

series137.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (/ 1.0 (* x 9.0)) y)
33.0ms	(* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0))
15.0ms	(/ 1.0 (* x 9.0))
65.0ms	(* (* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0)) (sqrt x))

simplify52.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	418	605
1	1918	533
2	5003	531

prune212.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes115.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	7
1	20	7

end0.0ms

sample1.3s

Algorithm

intervals

Results

526.0ms	8564×	body	80	valid
461.0ms	8626×	body	80	nan