Details

sample237.0ms

Algorithm

intervals

Results

166.0ms	100×	body	2560	valid
44.0ms	78×	body	1280	valid
8.0ms	39×	body	640	valid
5.0ms	256×	pre	80	true
3.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	3×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	8
1	11	8

prune2.0ms

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: 59.6b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.7b	(- (/ 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))
13.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series32.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(/ 1.0 (tan x))
21.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5145	561

prune86.0ms

Filtered

45 candidates to 56 candidates (-24.4%)

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: 0.3b

Counts

57 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

7.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))
6.0ms	(* 0.022222222222222223 (pow x 3))
5.0ms	(* 0.0021164021164021165 (pow x 5))

series29.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
12.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))
4.0ms	(* 0.022222222222222223 (pow x 3))
5.0ms	(* 0.0021164021164021165 (pow x 5))

simplify48.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5138	884

prune154.0ms

Filtered

60 candidates to 92 candidates (-53.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	6	93

Merged error: 0.1b

Counts

93 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

11.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
58.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
58.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
57.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

simplify35.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5046	2298

prune446.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	94	11	105

Merged error: 0.1b

Counts

105 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.6b	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.6b	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.6b	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
14×	`cbrt-div`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
5.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
5.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
5.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
77.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
77.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
77.0ms	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

simplify30.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5233	1801

prune538.0ms

Filtered

69 candidates to 73 candidates (-5.8%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	71	13	84

Merged error: 0.1b

Counts

84 → 13

regimes99.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms

sample7.3s

Algorithm

intervals

Results

5.2s	3265×	body	2560	valid
1.4s	2521×	body	1280	valid
245.0ms	1192×	body	640	valid
132.0ms	8000×	pre	80	true
83.0ms	648×	body	320	valid
29.0ms	326×	body	160	valid
2.0ms	48×	body	80	valid

Details

sample237.0ms

simplify3.0ms

prune2.0ms

localize10.0ms

rewrite19.0ms

series32.0ms

simplify57.0ms

prune86.0ms

localize10.0ms

rewrite25.0ms

series29.0ms

simplify48.0ms

prune154.0ms

localize15.0ms

rewrite28.0ms

series236.0ms

simplify35.0ms

prune446.0ms

localize20.0ms

rewrite20.0ms

series289.0ms

simplify30.0ms

prune538.0ms

regimes99.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.3s

Profiling