Details

sample80.0ms

Algorithm

intervals

Results

39.0ms

541×

body

valid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

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

prune19.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 4.9b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.2b	(* (* 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))))
4.3b	(* (* (* 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:

24.0ms	(* (* x 18.0) y)
34.0ms	(* (* 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))))
39.0ms	(* (* (* x 18.0) y) z)

simplify72.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (16.0ms)

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

prune479.0ms

Filtered

135 candidates to 97 candidates (71.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	126	9	135
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	9	137

Merged error: 2.5b

Counts

137 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.2b	(* 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)))))
4.3b	(* (* (* x 18.0) y) z)

rewrite39.0ms

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)
9.0ms	(* 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)))))
18.0ms	(* (* (* x 18.0) y) z)

series3.1s

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* x 18.0) y)
20.0ms	(* 27.0 (* j k))
3.0s	(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)

simplify87.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (19.0ms)

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

prune495.0ms

Filtered

135 candidates to 98 candidates (72.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	136	8	144

Merged error: 2.5b

Counts

144 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.2b	(* (* 27.0 k) j)
3.1b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* 27.0 k) j))))
4.3b	(* (* (* x 18.0) y) z)

rewrite34.0ms

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

series3.2s

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* x 18.0) y)
24.0ms	(* (* 27.0 k) j)
3.1s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* 27.0 k) j))))
33.0ms	(* (* (* x 18.0) y) z)

simplify84.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	449	639
1	1957	556
2	5001	556

prune517.0ms

Filtered

135 candidates to 98 candidates (72.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	135	8	143

Merged error: 2.5b

Counts

143 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* 27.0 k))
0.6b	(cbrt (* 27.0 k))
3.1b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* (cbrt (* 27.0 k)) (cbrt (* 27.0 k))) (* (cbrt (* 27.0 k)) j)))))
4.3b	(* (* (* x 18.0) y) z)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

43×	`associate-l`
36×	`add-sqr-sqrt`
24×	`cbrt-prod`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`unswap-sqr`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3`
1×	`fma-udef`

Counts

4 → 101

Calls

4 calls:

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

series3.8s

Counts

4 → 12

Calls

4 calls:

253.0ms	(cbrt (* 27.0 k))
259.0ms	(cbrt (* 27.0 k))
3.3s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* (cbrt (* 27.0 k)) (cbrt (* 27.0 k))) (* (cbrt (* 27.0 k)) j)))))
33.0ms	(* (* (* x 18.0) y) z)

simplify67.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	369	689
1	1313	612
2	5002	604

prune482.0ms

Filtered

113 candidates to 88 candidates (77.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	113	8	121

Merged error: 2.5b

Counts

121 → 8

regimes1.0s

Accuracy

32.7% (2.2b remaining)

Error of 4.4b against oracle of 2.2b and baseline of 5.5b

bsearch311.0ms

Steps

Iters	Range		Point
7	1.1447783026663262e-123	5.21564604304815e-122	1.9933044631699316e-123
9	-7.73677596798217e-67	-9.426574569238346e-74	-2.998995372134782e-73

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	33
1	67	33
2	67	33

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s

16209×

body

valid