Details

sample94.0ms

Algorithm

intervals

Results

42.0ms	860×	body	80	nan
14.0ms	256×	body	80	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

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: 1.2b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (/ x (* y 27.0)))
1.0b	(* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
3.6b	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
4.2b	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-exp-log` `add-cbrt-cube`
39×	`prod-exp` `cbrt-unprod`
29×	`add-sqr-sqrt`
27×	`cbrt-undiv` `div-exp`
21×	`associate-l`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
15×	`times-frac`
10×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
2×	`associate-r/` `associate-l/`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/l/` `associate-/l`

Counts

4 → 138

Calls

4 calls:

8.0ms	(* 3.0 (/ x (* y 27.0)))
7.0ms	(* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
14.0ms	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
10.0ms	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

series190.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* 3.0 (/ x (* y 27.0)))
23.0ms	(* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
111.0ms	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
34.0ms	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	750	1428
1	4297	1113
2	5001	1108

prune382.0ms

Filtered

150 candidates to 87 candidates (58.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	4	151

Merged error: 0b

Counts

151 → 4

localize19.0ms

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))
3.6b	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
4.2b	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

rewrite46.0ms

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×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `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 → 160

Calls

4 calls:

8.0ms	(* (/ 1.0 (cbrt 3.0)) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
4.0ms	(/ 1.0 (cbrt 3.0))
15.0ms	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
11.0ms	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

series229.0ms

Counts

4 → 10

Calls

4 calls:

88.0ms	(* (/ 1.0 (cbrt 3.0)) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
0.0ms	(/ 1.0 (cbrt 3.0))
105.0ms	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
35.0ms	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

simplify115.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	765	1691
1	4105	1399
2	5002	1394

prune601.0ms

Filtered

170 candidates to 114 candidates (67.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	171	3	174

Merged error: 0b

Counts

174 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* 1.0 (/ (acos (* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))) (cbrt 3.0))))
0.2b	(* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))
3.6b	(* (sqrt t) (/ x (* z y)))
5.6b	(/ x (* z y))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log`
59×	`add-cbrt-cube`
57×	`prod-exp`
31×	`cbrt-unprod`
25×	`div-exp`
17×	`add-sqr-sqrt`
16×	`pow1` `associate-l`
15×	`cbrt-undiv`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac` `associate-r`
7×	`pow-prod-down`
6×	`rec-exp` `1-exp` `associate-*r/`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
2×	`unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `associate-/r`

Counts

4 → 134

Calls

4 calls:

16.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* 1.0 (/ (acos (* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))) (cbrt 3.0))))
11.0ms	(* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))
14.0ms	(* (sqrt t) (/ x (* z y)))
6.0ms	(/ x (* z y))

series304.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* 1.0 (/ (acos (* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))) (cbrt 3.0))))
85.0ms	(* 0.05555555555555555 (* (sqrt t) (/ x (* z y))))
82.0ms	(* (sqrt t) (/ x (* z y)))
24.0ms	(/ x (* z y))

simplify109.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	726	1568
1	3457	1191
2	5001	1106

prune412.0ms

Filtered

146 candidates to 82 candidates (56.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	146	3	149

Merged error: 0b

Counts

149 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ 1.0 3.0) (acos (log (exp (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))))
3.6b	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
4.2b	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))
4.6b	(log (exp (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-exp-log` `add-cbrt-cube`
35×	`prod-exp` `cbrt-unprod`
25×	`cbrt-undiv` `add-sqr-sqrt` `div-exp`
18×	`associate-l`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
9×	`pow1` `associate-r`
5×	`add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `log-pow` `div-inv`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`exp-prod` `exp-to-pow` `frac-2neg` `associate-r/` `rem-log-exp` `clear-num` `associate-/r` `associate-/l/` `associate-/l*`

Counts

4 → 125

Calls

4 calls:

7.0ms	(* (/ 1.0 3.0) (acos (log (exp (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))))
15.0ms	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
11.0ms	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))
2.0ms	(log (exp (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (/ 1.0 3.0) (acos (log (exp (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))))
109.0ms	(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
32.0ms	(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))
113.0ms	(log (exp (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))

simplify112.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	716	1566
1	3953	1243
2	5002	1235

prune381.0ms

Filtered

137 candidates to 82 candidates (59.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	138	2	140

Merged error: 0b

Counts

140 → 2

regimes220.0ms

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	27	14
1	27	14

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	24163×	body	80	nan
446.0ms	8000×	body	80	valid