Details

sample33.0ms

Algorithm

intervals

Results

10.0ms	296×	body	80	nan
9.0ms	272×	body	80	valid

simplify115.0ms

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: 0.4b

localize9.0ms

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))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(* 3.0 (sqrt x))

rewrite194.0ms

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:

10.0ms	(+ y (/ 1.0 (* x 9.0)))
163.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
7.0ms	(/ 1.0 (* x 9.0))
9.0ms	(* 3.0 (sqrt x))

series129.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ y (/ 1.0 (* x 9.0)))
56.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
14.0ms	(/ 1.0 (* x 9.0))
36.0ms	(* 3.0 (sqrt x))

simplify73.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (62.0ms)

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

prune348.0ms

Pruning

16 alts after pruning (16 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	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

rewrite397.0ms

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:

11.0ms	(+ y (/ 1.0 (* x 9.0)))
183.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
7.0ms	(/ 1.0 (* x 9.0))
188.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ y (/ 1.0 (* x 9.0)))
54.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
14.0ms	(/ 1.0 (* x 9.0))
59.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (59.0ms)

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

prune379.0ms

Pruning

12 alts after pruning (12 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	(* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
0.2b	(/ (/ 1.0 x) 9.0)
0.3b	(* 3.0 (* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0)))

rewrite814.0ms

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:

22.0ms	(+ y (/ (/ 1.0 x) 9.0))
399.0ms	(* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
10.0ms	(/ (/ 1.0 x) 9.0)
372.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ y (/ (/ 1.0 x) 9.0))
49.0ms	(* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
21.0ms	(/ (/ 1.0 x) 9.0)
56.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0)))

simplify105.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	856	2770
1	3565	2116
2	5002	2110

prune578.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
21×	`pow1`
18×	`add-exp-log` `times-frac` `add-cbrt-cube`
16×	`associate-r`
13×	`associate-l`
12×	`swap-sqr`
8×	`sqrt-pow1` `pow1/2`
6×	`div-inv` `associate-/l*` `unswap-sqr`
5×	`pow-prod-up`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `rem-square-sqrt`

Counts

4 → 136

Calls

4 calls:

7.0ms	(/ 1.0 (* x 9.0))
8.0ms	(/ 1.0 (* x 9.0))
9.0ms	(* 3.0 (sqrt x))
43.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 1.0 (* x 9.0))
15.0ms	(/ 1.0 (* x 9.0))
33.0ms	(* 3.0 (sqrt x))
55.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

simplify59.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	384	624
1	1873	540
2	5001	527

prune437.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes123.0ms

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	15	7
1	15	7

end0.0ms

sample859.0ms

Algorithm

intervals

Results

289.0ms	8581×	body	80	valid
284.0ms	8487×	body	80	nan