Details

sample76.0ms

Algorithm

intervals

Results

38.0ms

510×

body

valid

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	67	15
1	225	13
2	823	12
3	3028	12
4	5001	12

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 5.9b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.4b	(* (* j 27.0) k)
3.1b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
5.5b	(* (* (* x 18.0) y) z)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

67×	`associate-l`
48×	`add-sqr-sqrt`
23×	`pow1` `add-exp-log` `add-cbrt-cube`
21×	`associate-r`
18×	`add-cube-cbrt` `*-un-lft-identity` `unswap-sqr`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

4 → 123

Calls

4 calls:

8.0ms	(* (* x 18.0) y)
8.0ms	(* (* j 27.0) k)
1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
14.0ms	(* (* (* x 18.0) y) z)

series3.0s

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* x 18.0) y)
20.0ms	(* (* j 27.0) k)
2.9s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
33.0ms	(* (* (* x 18.0) y) z)

simplify67.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	450	639
1	1938	556
2	5001	556

prune682.0ms

Filtered

135 candidates to 97 candidates (71.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	128	7	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	7	136

Merged error: 1.8b

Counts

136 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.3b	(* 27.0 (* j k))
3.1b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* 27.0 (* j k)))))
5.5b	(* (* (* x 18.0) y) z)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

58×	`associate-l`
48×	`add-sqr-sqrt`
30×	`associate-r`
23×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`add-cube-cbrt` `*-un-lft-identity` `unswap-sqr`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

4 → 123

Calls

4 calls:

8.0ms	(* (* x 18.0) y)
13.0ms	(* 27.0 (* j k))
1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* 27.0 (* j k)))))
15.0ms	(* (* (* x 18.0) y) z)

series3.0s

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* x 18.0) y)
19.0ms	(* 27.0 (* j k))
2.9s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* 27.0 (* j k)))))
30.0ms	(* (* (* x 18.0) y) z)

simplify72.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	459	641
1	2132	558
2	5001	558

prune678.0ms

Filtered

135 candidates to 98 candidates (72.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	137	5	142

Merged error: 1.8b

Counts

142 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 27.0) (* j k))
0.3b	(* (sqrt 27.0) (* (sqrt 27.0) (* j k)))
3.1b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (sqrt 27.0) (* (sqrt 27.0) (* j k))))))
5.5b	(* (* (* x 18.0) y) z)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
66×	`associate-r`
61×	`associate-l`
46×	`unswap-sqr`
27×	`pow1` `add-exp-log` `add-cbrt-cube`
23×	`add-cube-cbrt` `*-un-lft-identity`
22×	`sqrt-prod`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

4 → 157

Calls

4 calls:

14.0ms	(* (sqrt 27.0) (* j k))
20.0ms	(* (sqrt 27.0) (* (sqrt 27.0) (* j k)))
1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (sqrt 27.0) (* (sqrt 27.0) (* j k))))))
14.0ms	(* (* (* x 18.0) y) z)

series3.6s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sqrt 27.0) (* j k))
87.0ms	(* (sqrt 27.0) (* (sqrt 27.0) (* j k)))
3.5s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (sqrt 27.0) (* (sqrt 27.0) (* j k))))))
30.0ms	(* (* (* x 18.0) y) z)

simplify89.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	574	1045
1	2607	870
2	5001	864

prune760.0ms

Filtered

169 candidates to 108 candidates (63.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	169	5	174

Merged error: 1.8b

Counts

174 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 18.0 (* x y))
0.4b	(* (* j 27.0) k)
3.1b	(fma t (- (* (* 18.0 (* x y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
5.5b	(* (* 18.0 (* x y)) z)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

49×	`associate-l`
48×	`add-sqr-sqrt`
39×	`associate-r`
23×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`add-cube-cbrt` `*-un-lft-identity` `unswap-sqr`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

4 → 123

Calls

4 calls:

8.0ms	(* 18.0 (* x y))
8.0ms	(* (* j 27.0) k)
1.0ms	(fma t (- (* (* 18.0 (* x y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
14.0ms	(* (* 18.0 (* x y)) z)

series3.1s

Counts

4 → 12

Calls

4 calls:

22.0ms	(* 18.0 (* x y))
33.0ms	(* (* j 27.0) k)
3.0s	(fma t (- (* (* 18.0 (* x y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
33.0ms	(* (* 18.0 (* x y)) z)

simplify69.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	457	635
1	2053	552
2	5002	552

prune632.0ms

Filtered

135 candidates to 94 candidates (69.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	135	5	140

Merged error: 1.8b

Counts

140 → 5

regimes798.0ms

Accuracy

52.1% (1.3b remaining)

Error of 4.3b against oracle of 3.0b and baseline of 5.8b

bsearch243.0ms

Steps

Iters	Range		Point
9	5.633863048964624e-132	5.6274658287191175e-126	1.6425602788359552e-131
6	-2.7036907453770258e-114	-1.6902579985282683e-115	-2.42866793610458e-115

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	33
1	63	33
2	63	33

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s

16062×

body

valid