Details

sample184.0ms

Algorithm

intervals

Results

117.0ms	95×	body	2560	valid
45.0ms	89×	body	1280	valid
6.0ms	34×	body	640	valid
4.0ms	256×	pre	80	true
3.0ms	30×	body	320	valid
0.0ms	6×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	11	4
2	11	4

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: 59.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.9b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`tan-quot` `cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 50

Calls

2 calls:

4.0ms	(/ 1.0 (tan x))
14.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series133.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ 1.0 (tan x))
99.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify58.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	232	342
1	610	327
2	1894	327
3	5001	326

prune101.0ms

Filtered

56 candidates to 46 candidates (82.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	1	57

Merged error: 0.4b

Counts

57 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

8.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
5.0ms	(* 0.0021164021164021165 (pow x 5))
9.0ms	(* 0.022222222222222223 (pow x 3))

series142.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
51.0ms	(* 0.0021164021164021165 (pow x 5))
35.0ms	(* 0.022222222222222223 (pow x 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	301	381
1	1298	348
2	5002	348

prune145.0ms

Filtered

78 candidates to 49 candidates (62.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Merged error: 0.3b

Counts

79 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (log (exp (* 0.0021164021164021165 (pow x 5)))) (* 0.3333333333333333 x)))
0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))
1.4b	(log (exp (* 0.0021164021164021165 (pow x 5))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`pow1`
4×	`cube-prod` `sqr-pow`
3×	`log-prod` `sum-log` `log-pow`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `exp-prod` `exp-to-pow` `flip3-+` `unpow3` `rem-log-exp` `flip-+`

Counts

4 → 83

Calls

4 calls:

8.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (log (exp (* 0.0021164021164021165 (pow x 5)))) (* 0.3333333333333333 x)))
6.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))
2.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (log (exp (* 0.0021164021164021165 (pow x 5)))) (* 0.3333333333333333 x)))
51.0ms	(* 0.0021164021164021165 (pow x 5))
34.0ms	(* 0.022222222222222223 (pow x 3))
50.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))

simplify46.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	328	478
1	1386	421
2	5001	421

prune204.0ms

Filtered

95 candidates to 60 candidates (63.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	95	6	101

Merged error: 0.3b

Counts

101 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))
1.3b	(log (exp (* 0.022222222222222223 (pow x 3))))
1.4b	(log (exp (* 0.0021164021164021165 (pow x 5))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`pow1` `log-prod` `associate-l` `prod-exp` `log-pow` `add-log-exp`
4×	`cube-prod` `sqr-pow`
2×	`pow-to-exp` `exp-prod` `exp-to-pow` `rem-log-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`cube-mult` `unpow3`

Counts

4 → 84

Calls

4 calls:

5.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))
2.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))
2.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))

series173.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* 0.0021164021164021165 (pow x 5))
41.0ms	(* 0.022222222222222223 (pow x 3))
35.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))
52.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))

simplify193.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	243	347
1	915	305
2	4712	305
3	5002	305

prune222.0ms

Filtered

96 candidates to 62 candidates (64.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	96	6	102

Merged error: 0.3b

Counts

102 → 6

regimes29.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	18
1	24	18

end0.0ms

sample7.1s

Algorithm

intervals

Results

5.2s	3259×	body	2560	valid
1.3s	2455×	body	1280	valid
233.0ms	1244×	body	640	valid
128.0ms	8000×	pre	80	true
72.0ms	651×	body	320	valid
25.0ms	326×	body	160	valid
3.0ms	65×	body	80	valid