Details

sample279.0ms

Algorithm

intervals

Results

11.0ms	42×	body	1280	valid
8.0ms	150×	body	80	valid
6.0ms	33×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	13×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9

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: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	917
2	5001	882

prune279.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Merged error: 0.0b

Counts

132 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
0.3b	(* (tan x) (tan x))
0.7b	(pow (tan x) 6)
9.2b	(cbrt (pow (tan x) 6))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
16×	`times-frac`
12×	`pow1`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`cbrt-prod`
6×	`unpow-prod-down`
5×	`distribute-lft-out` `difference-of-squares`
4×	`tan-quot` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow2` `frac-times` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `pow-plus` `pow1/3` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

12.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
5.0ms	(* (tan x) (tan x))
3.0ms	(pow (tan x) 6)
3.0ms	(cbrt (pow (tan x) 6))

series216.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
31.0ms	(* (tan x) (tan x))
61.0ms	(pow (tan x) 6)
32.0ms	(cbrt (pow (tan x) 6))

simplify58.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	415	955
1	1674	883
2	5002	844

prune245.0ms

Filtered

121 candidates to 82 candidates (67.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	122	12	134

Merged error: 0.0b

Counts

134 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.2b	(/ 1 (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt`
21×	`pow1` `add-exp-log` `associate-r`
20×	`times-frac`
15×	`add-cbrt-cube`
10×	`associate-l`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `associate-/r` `-commutative` `associate-/l`
2×	`cbrt-undiv` `pow2` `rec-exp` `flip3--` `flip3-+` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `flip--` `flip-+` `div-inv`
1×	`pow-flip` `frac-2neg` `clear-num` `un-div-inv` `inv-pow` `difference-of-squares`

Counts

4 → 140

Calls

4 calls:

10.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
53.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))

simplify59.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	404	1182
1	1847	1017
2	5001	958

prune225.0ms

Filtered

152 candidates to 94 candidates (61.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	152	12	164

Merged error: 0.0b

Counts

164 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (tan x) 6)
0.7b	(pow (tan x) 6)
9.2b	(cbrt (pow (tan x) 6))
9.2b	(cbrt (pow (tan x) 6))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `pow-unpow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow (tan x) 6)
3.0ms	(pow (tan x) 6)
2.0ms	(cbrt (pow (tan x) 6))
3.0ms	(cbrt (pow (tan x) 6))

series187.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (tan x) 6)
62.0ms	(pow (tan x) 6)
31.0ms	(cbrt (pow (tan x) 6))
35.0ms	(cbrt (pow (tan x) 6))

simplify104.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	147	396
1	486	350
2	2205	340
3	5001	306

prune173.0ms

Filtered

84 candidates to 58 candidates (69.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	84	12	96

Merged error: 0.0b

Counts

96 → 12

regimes158.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	10
1	13	10

end0.0ms

sample979.0ms

Algorithm

intervals

Results

376.0ms	1468×	body	1280	valid
209.0ms	1258×	body	640	valid
165.0ms	4314×	body	80	valid
80.0ms	639×	body	320	valid
32.0ms	321×	body	160	valid