Details

sample32.0ms

Algorithm

intervals

Results

10.0ms	319×	body	80	nan
9.0ms	284×	body	80	valid

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 0.4b

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	(* 3.0 (sqrt x))
0.4b	(/ 1.0 (* x 9.0))

rewrite84.0ms

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)))
70.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
4.0ms	(* 3.0 (sqrt x))
3.0ms	(/ 1.0 (* x 9.0))

series152.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
67.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
41.0ms	(* 3.0 (sqrt x))
18.0ms	(/ 1.0 (* x 9.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (49.0ms)

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

prune206.0ms

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	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
0.4b	(/ 1.0 (* x 9.0))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

5.0ms	(+ y (/ 1.0 (* x 9.0)))
80.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
72.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
3.0ms	(/ 1.0 (* x 9.0))

series171.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ y (/ 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)))
17.0ms	(/ 1.0 (* x 9.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	427	770
1	1858	694
2	5002	694

prune213.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
0.4b	(/ 1.0 (* x 9.0))
0.4b	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 143

Calls

4 calls:

80.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
204.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
3.0ms	(/ 1.0 (* x 9.0))
75.0ms	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
96.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
16.0ms	(/ 1.0 (* x 9.0))
136.0ms	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	681	1766
1	2737	1381
2	5003	1319

prune272.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x)))
0.4b	(/ 1.0 (* x 9.0))
0.4b	(* (cbrt 3.0) (sqrt x))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
36×	`pow1`
28×	`add-cbrt-cube`
23×	`prod-exp` `cbrt-unprod`
22×	`pow-prod-down`
21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`associate-r`
11×	`add-cube-cbrt`
8×	`associate-l`
5×	`cbrt-prod` `sqrt-prod`
4×	`add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `-commutative` `associate-/l`
2×	`cbrt-undiv` `sub-neg` `associate-*r/` `div-exp` `associate--l+` `distribute-lft-out--`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r*` `flip--` `div-inv` `distribute-lft-out` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

131.0ms	(* (* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
19.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x)))
3.0ms	(/ 1.0 (* x 9.0))
6.0ms	(* (cbrt 3.0) (sqrt x))

series263.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
79.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x)))
16.0ms	(/ 1.0 (* x 9.0))
69.0ms	(* (cbrt 3.0) (sqrt x))

simplify87.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	573	1128
1	3010	841
2	5001	776

prune234.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes116.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample828.0ms

Algorithm

intervals

Results

286.0ms	8717×	body	80	nan
274.0ms	8548×	body	80	valid