Details

sample52.0ms

Algorithm

intervals

Results

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

simplify110.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 0.3b

localize9.0ms

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))

rewrite94.0ms

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)))
4.0ms	(* 3.0 (sqrt x))
78.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
3.0ms	(/ 1.0 (* x 9.0))

series139.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ y (/ 1.0 (* x 9.0)))
35.0ms	(* 3.0 (sqrt x))
62.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
15.0ms	(/ 1.0 (* x 9.0))

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

prune243.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma 0.1111111111111111 (/ 1 x) y) 1.0)
0.2b	(fma 0.1111111111111111 (/ 1 x) y)
0.2b	(* 3.0 (sqrt x))
0.3b	(* (* 3.0 (sqrt x)) (- (fma 0.1111111111111111 (/ 1 x) y) 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt` `prod-diff`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `fma-udef` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `associate--l+`
2×	`flip3--` `associate-r/` `-commutative` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`diff-log`

Counts

4 → 111

Calls

4 calls:

3.0ms	(- (fma 0.1111111111111111 (/ 1 x) y) 1.0)
0.0ms	(fma 0.1111111111111111 (/ 1 x) y)
4.0ms	(* 3.0 (sqrt x))
17.0ms	(* (* 3.0 (sqrt x)) (- (fma 0.1111111111111111 (/ 1 x) y) 1.0))

series162.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(- (fma 0.1111111111111111 (/ 1 x) y) 1.0)
29.0ms	(fma 0.1111111111111111 (/ 1 x) y)
37.0ms	(* 3.0 (sqrt x))
70.0ms	(* (* 3.0 (sqrt x)) (- (fma 0.1111111111111111 (/ 1 x) y) 1.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	472	1070
1	2206	801
2	5001	778

prune234.0ms

Pruning

13 alts after pruning (12 fresh and 1 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))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`sqrt-prod`
33×	`add-cube-cbrt`
24×	`pow1`
21×	`add-exp-log` `add-cbrt-cube`
18×	`times-frac` `prod-diff`
15×	`associate-r`
12×	`distribute-rgt-in` `distribute-lft-in` `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` `expm1-log1p-u` `sqrt-div` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`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 → 160

Calls

4 calls:

32.0ms	(* (* 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))
24.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

series227.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (* 3.0 (sqrt x)) (- (+ y (* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))) 1.0))
16.0ms	(/ 1.0 (* x 9.0))
16.0ms	(/ 1.0 (* x 9.0))
60.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

simplify105.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	647	1613
1	3382	1187
2	5001	1138

prune384.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

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))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
26×	`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`
7×	`fma-def`
6×	`times-frac` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-r/` `associate-l*` `pow-prod-down` `log1p-expm1-u`
3×	`sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `flip3--` `div-exp` `associate-l/` `associate--l+` `-commutative` `flip--` `div-inv` `distribute-lft-out--`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `associate-/r*` `sum-log` `flip-+` `difference-of-squares` `unswap-sqr`

Counts

4 → 124

Calls

4 calls:

9.0ms	(+ (/ 1.0 (* x 9.0)) y)
125.0ms	(* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0))
3.0ms	(/ 1.0 (* x 9.0))
133.0ms	(* (* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0)) (sqrt x))

series136.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (/ 1.0 (* x 9.0)) y)
28.0ms	(* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0))
22.0ms	(/ 1.0 (* x 9.0))
62.0ms	(* (* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0)) (sqrt x))

simplify70.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	505	1097
1	2390	832
2	5003	827

prune314.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes135.0ms

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	27	13
1	27	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

540.0ms	8564×	body	80	valid
473.0ms	8626×	body	80	nan