Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	275×	body	80	valid
7.0ms	243×	body	80	nan

simplify108.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.4b

Counts

2 → 1

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))
0.5b	(/ 1.0 (* x 9.0))

rewrite31.0ms

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)))
13.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
5.0ms	(* 3.0 (sqrt x))
4.0ms	(/ 1.0 (* x 9.0))

series200.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ y (/ 1.0 (* x 9.0)))
98.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
47.0ms	(* 3.0 (sqrt x))
16.0ms	(/ 1.0 (* x 9.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (90.0ms)

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

prune313.0ms

Filtered

131 candidates to 75 candidates (57.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Merged error: 0.0b

Counts

132 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ 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)))
0.5b	(/ 1.0 (* x 9.0))

rewrite45.0ms

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)))
13.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
14.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
5.0ms	(/ 1.0 (* x 9.0))

series162.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
57.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
61.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
19.0ms	(/ 1.0 (* x 9.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	633	2404
1	2663	1754
2	5002	1748

prune274.0ms

Filtered

193 candidates to 84 candidates (43.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	193	13	206

Merged error: 0b

Counts

206 → 13

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))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 168

Calls

4 calls:

13.0ms	(+ y (/ (/ 1.0 x) 9.0))
21.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
6.0ms	(/ (/ 1.0 x) 9.0)
5.0ms	(* 3.0 (sqrt x))

series146.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ y (/ (/ 1.0 x) 9.0))
62.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
16.0ms	(/ (/ 1.0 x) 9.0)
41.0ms	(* 3.0 (sqrt x))

simplify102.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	818	1496
1	3749	1238
2	5001	1234

prune395.0ms

Filtered

180 candidates to 118 candidates (65.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	174	6	180
Fresh	6	5	11
Picked	1	0	1
Done	0	1	1
Total	181	12	193

Merged error: 0b

Counts

193 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (sqrt 1.0) (sqrt x)) (cbrt 9.0))
0.3b	(* 3.0 (sqrt x))
0.3b	(/ (/ (sqrt 1.0) (sqrt x)) (* (cbrt 9.0) (cbrt 9.0)))
0.4b	(* (/ (/ (sqrt 1.0) (sqrt x)) (* (cbrt 9.0) (cbrt 9.0))) (/ (/ (sqrt 1.0) (sqrt x)) (cbrt 9.0)))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

1343×	`times-frac`
859×	`add-sqr-sqrt`
672×	`sqrt-prod`
571×	`add-cube-cbrt` `*-un-lft-identity`
273×	`cbrt-prod`
250×	`associate-r`
92×	`add-exp-log`
80×	`associate-/l*`
68×	`unswap-sqr`
64×	`add-cbrt-cube`
47×	`associate-l`
42×	`cbrt-undiv` `div-exp`
24×	`prod-exp` `cbrt-unprod`
20×	`div-inv`
8×	`pow1`
7×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/`
1×	`frac-times` `associate-r/` `associate-l/`

Counts

4 → 827

Calls

4 calls:

15.0ms	(/ (/ (sqrt 1.0) (sqrt x)) (cbrt 9.0))
5.0ms	(* 3.0 (sqrt x))
14.0ms	(/ (/ (sqrt 1.0) (sqrt x)) (* (cbrt 9.0) (cbrt 9.0)))
175.0ms	(* (/ (/ (sqrt 1.0) (sqrt x)) (* (cbrt 9.0) (cbrt 9.0))) (/ (/ (sqrt 1.0) (sqrt x)) (cbrt 9.0)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (/ (sqrt 1.0) (sqrt x)) (cbrt 9.0))
37.0ms	(* 3.0 (sqrt x))
180.0ms	(/ (/ (sqrt 1.0) (sqrt x)) (* (cbrt 9.0) (cbrt 9.0)))
169.0ms	(* (/ (/ (sqrt 1.0) (sqrt x)) (* (cbrt 9.0) (cbrt 9.0))) (/ (/ (sqrt 1.0) (sqrt x)) (cbrt 9.0)))

simplify151.0ms

Algorithm

egg-herbie

Counts

839 → 839

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2595	12371
1	5002	11827

prune2.1s

Filtered

839 candidates to 430 candidates (51.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	838	1	839
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	839	12	851

Merged error: 0b

Counts

851 → 12

regimes90.0ms

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	16	7
1	16	7

end0.0ms

sample849.0ms

Algorithm

intervals

Results

283.0ms	8515×	body	80	valid
273.0ms	8653×	body	80	nan