Details

sample32.0ms

Algorithm

intervals

Results

9.0ms	303×	body	80	nan
8.0ms	272×	body	80	valid

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	7
1	65	7
2	190	7
3	412	7
4	644	7
5	1083	7
6	1628	7
7	2273	7
8	3723	7
9	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
24×	`prod-diff`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-r`
11×	`pow1`
8×	`distribute-lft-out`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `associate-r/` `div-exp` `associate--l+` `-commutative` `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 → 119

Calls

4 calls:

5.0ms	(+ y (/ 1.0 (* x 9.0)))
82.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
3.0ms	(/ 1.0 (* x 9.0))
5.0ms	(* 3.0 (sqrt x))

series149.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ y (/ 1.0 (* x 9.0)))
62.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
20.0ms	(/ 1.0 (* x 9.0))
37.0ms	(* 3.0 (sqrt x))

simplify74.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	594	1130
1	2888	878
2	5001	872

prune285.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
75×	`distribute-rgt-in` `distribute-lft-in`
72×	`prod-diff`
59×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
20×	`distribute-lft-out`
16×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`associate-l`
7×	`associate-r`
6×	`sub-neg` `associate-*r/` `associate--l+` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `associate-/r*` `sum-log` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 181

Calls

4 calls:

5.0ms	(+ y (/ 1.0 (* x 9.0)))
3.0ms	(/ 1.0 (* x 9.0))
91.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
97.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
16.0ms	(/ 1.0 (* x 9.0))
61.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
67.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	633	2404
1	2665	1754
2	5002	1748

prune287.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite660.0ms

Algorithm

rewrite-expression-head

Rules

136×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
93×	`add-cube-cbrt`
75×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
72×	`prod-diff`
20×	`distribute-lft-out`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
11×	`pow1`
9×	`associate-l`
7×	`associate-r`
6×	`sub-neg` `associate-*r/` `associate--l+` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `div-exp` `associate-/r*`
2×	`flip3--` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `associate-/l/` `difference-of-squares`

Counts

4 → 230

Calls

4 calls:

16.0ms	(+ y (/ (/ 1.0 x) 9.0))
6.0ms	(/ (/ 1.0 x) 9.0)
321.0ms	(* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
303.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ y (/ (/ 1.0 x) 9.0))
16.0ms	(/ (/ 1.0 x) 9.0)
61.0ms	(* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
62.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0)))

simplify107.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	856	2770
1	3565	2116
2	5001	2110

prune447.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`associate-l`
14×	`-un-lft-identity` `associate-r*`
12×	`add-cube-cbrt`
8×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-l/` `-commutative` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`times-frac` `difference-of-squares`
2×	`flip3--` `associate-*r/` `flip--`
1×	`distribute-lft-out--`

Counts

4 → 96

Calls

4 calls:

105.0ms	(* (- (/ (/ 1.0 x) 9.0) 1.0) (sqrt x))
8.0ms	(* 3.0 (* y (sqrt x)))
4.0ms	(* y (sqrt x))
108.0ms	(* 3.0 (* (- (/ (/ 1.0 x) 9.0) 1.0) (sqrt x)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (- (/ (/ 1.0 x) 9.0) 1.0) (sqrt x))
52.0ms	(* 3.0 (* y (sqrt x)))
44.0ms	(* y (sqrt x))
73.0ms	(* 3.0 (* (- (/ (/ 1.0 x) 9.0) 1.0) (sqrt x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	426	699
1	1758	603
2	5002	587

prune247.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

regimes98.0ms

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	19	10
1	19	10

end0.0ms

sample802.0ms

Algorithm

intervals

Results

262.0ms	8569×	body	80	valid
260.0ms	8729×	body	80	nan