Details

sample283.0ms

Algorithm

intervals

Results

14.0ms	47×	body	1280	valid
6.0ms	36×	body	640	valid
6.0ms	149×	body	80	valid
2.0ms	19×	body	320	valid
0.0ms	5×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (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:

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

series223.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	918
2	5001	882

prune271.0ms

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

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

10.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series198.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
33.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))

simplify64.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	406	1046
1	1794	921
2	5002	874

prune226.0ms

Filtered

138 candidates to 88 candidates (63.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	138	13	151

Merged error: 0.0b

Counts

151 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
76×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
13×	`difference-of-squares`
12×	`pow1`
11×	`add-cbrt-cube`
9×	`associate-/r/`
7×	`div-exp`
6×	`add-log-exp`
5×	`flip3--` `flip--` `div-inv`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`pow2` `frac-times` `sub-neg` `pow-flip` `frac-2neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
3.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series225.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma (tan x) (tan x) 1.0)
33.0ms	(- 1.0 (* (tan x) (tan x)))
108.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
38.0ms	(* (tan x) (tan x))

simplify76.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	570	2046
1	2617	1859
2	5002	1752

prune272.0ms

Filtered

171 candidates to 97 candidates (56.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	171	13	184

Merged error: 0.0b

Counts

184 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(pow (cos x) 2)
0.2b	(* (tan x) (tan x))
0.2b	(pow (sin x) 2)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1`
8×	`add-exp-log`
6×	`unpow-prod-down` `pow-unpow` `add-cbrt-cube` `add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff`
2×	`pow-to-exp` `pow-pow` `pow-exp` `unpow2` `sqr-pow`
1×	`pow2` `frac-times` `sub-neg` `flip3--` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
2.0ms	(pow (cos x) 2)
5.0ms	(* (tan x) (tan x))
3.0ms	(pow (sin x) 2)

series107.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
17.0ms	(pow (cos x) 2)
37.0ms	(* (tan x) (tan x))
20.0ms	(pow (sin x) 2)

simplify154.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (146.0ms)

Iter	Nodes	Cost
0	293	451
1	1010	395
2	4646	386
3	5001	381

prune232.0ms

Filtered

103 candidates to 65 candidates (63.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	104	12	116

Merged error: 0.0b

Counts

116 → 12

regimes182.0ms

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

sample983.0ms

Algorithm

intervals

Results

402.0ms	1557×	body	1280	valid
205.0ms	1235×	body	640	valid
158.0ms	4281×	body	80	valid
76.0ms	648×	body	320	valid
23.0ms	279×	body	160	valid