Details

sample81.0ms

Algorithm

intervals

Results

36.0ms	721×	body	80	nan
13.0ms	256×	body	80	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	10
1	122	10
2	509	10
3	2237	10
4	5001	10

prune3.0ms

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: 1.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ x (* y 27.0))
1.0b	(* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
4.0b	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
5.6b	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-exp-log` `add-cbrt-cube`
36×	`prod-exp` `cbrt-unprod`
27×	`cbrt-undiv` `div-exp`
26×	`add-sqr-sqrt`
18×	`associate-l`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
9×	`associate-r`
8×	`pow1`
4×	`sqrt-prod` `div-inv` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `*-commutative`
1×	`associate-*r/` `associate-/l/`

Counts

4 → 124

Calls

4 calls:

4.0ms	(/ x (* y 27.0))
6.0ms	(* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
13.0ms	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
9.0ms	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

series157.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ x (* y 27.0))
16.0ms	(* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
91.0ms	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
31.0ms	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

simplify90.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	722	1318
1	3917	1017
2	5001	1015

prune258.0ms

Filtered

136 candidates to 77 candidates (56.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	3	137

Merged error: 0.0b

Counts

137 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ 1.0 (cbrt 3.0)) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
1.0b	(/ 1.0 (cbrt 3.0))
4.0b	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
5.6b	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-exp-log`
83×	`add-cbrt-cube`
48×	`add-sqr-sqrt`
40×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
35×	`prod-exp` `cbrt-unprod`
27×	`associate-l`
26×	`cbrt-undiv` `div-exp`
22×	`cbrt-prod`
9×	`associate-r`
8×	`pow1`
7×	`associate-/r*`
5×	`unswap-sqr`
4×	`sqrt-prod` `div-inv` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`
1×	`associate-*r/` `associate-/l/`

Counts

4 → 152

Calls

4 calls:

7.0ms	(* (/ 1.0 (cbrt 3.0)) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
4.0ms	(/ 1.0 (cbrt 3.0))
12.0ms	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
9.0ms	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

series202.0ms

Counts

4 → 10

Calls

4 calls:

79.0ms	(* (/ 1.0 (cbrt 3.0)) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
0.0ms	(/ 1.0 (cbrt 3.0))
93.0ms	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
30.0ms	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

simplify101.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	755	1633
1	4089	1341
2	5002	1339

prune429.0ms

Filtered

162 candidates to 106 candidates (65.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	162	3	165

Merged error: 0.0b

Counts

165 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.3333333333333333 (acos (* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))))
0.2b	(* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))
3.8b	(* (sqrt t) (/ x (* z y)))
7.0b	(/ x (* z y))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`prod-exp` `cbrt-unprod`
13×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
12×	`associate-l`
11×	`associate-r`
6×	`cbrt-undiv` `times-frac` `div-exp`
5×	`pow-prod-down`
4×	`sqrt-prod` `add-log-exp`
3×	`associate-r/` `-commutative` `associate-/l*` `unswap-sqr`
2×	`div-inv`
1×	`frac-2neg` `clear-num` `associate-/r*`

Counts

4 → 93

Calls

4 calls:

3.0ms	(* 0.3333333333333333 (acos (* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))))
9.0ms	(* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))
8.0ms	(* (sqrt t) (/ x (* z y)))
4.0ms	(/ x (* z y))

series181.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* 0.3333333333333333 (acos (* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))))
73.0ms	(* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))
71.0ms	(* (sqrt t) (/ x (* z y)))
21.0ms	(/ x (* z y))

simplify56.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	445	733
1	2061	610
2	5001	598

prune190.0ms

Filtered

105 candidates to 67 candidates (63.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	104	4	108

Merged error: 0b

Counts

108 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))
3.4b	(log (exp (* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))))
3.8b	(* (sqrt t) (/ x (* z y)))
7.0b	(/ x (* z y))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
13×	`prod-exp` `cbrt-unprod`
12×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`associate-r`
6×	`cbrt-undiv` `times-frac` `div-exp`
5×	`add-log-exp`
4×	`pow-prod-down` `sqrt-prod`
3×	`log-prod` `associate-r/` `log-pow` `associate-/l`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`exp-prod` `exp-to-pow` `frac-2neg` `rem-log-exp` `clear-num` `associate-/r*`

Counts

4 → 89

Calls

4 calls:

9.0ms	(* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))
2.0ms	(log (exp (* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))))
8.0ms	(* (sqrt t) (/ x (* z y)))
5.0ms	(/ x (* z y))

series240.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))
75.0ms	(log (exp (* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))))
72.0ms	(* (sqrt t) (/ x (* z y)))
21.0ms	(/ x (* z y))

simplify56.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	407	683
1	1911	567
2	5001	549

prune221.0ms

Filtered

101 candidates to 68 candidates (67.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	101	4	105

Merged error: 0b

Counts

105 → 4

regimes284.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	23643×	body	80	nan
401.0ms	8000×	body	80	valid