Details

sample279.0ms

Algorithm

intervals

Results

10.0ms	40×	body	1280	valid
6.0ms	41×	body	640	valid
5.0ms	142×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	12×	body	160	valid

simplify15.0ms

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))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite27.0ms

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))
8.0ms	(* (tan x) (tan x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
95.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (34.0ms)

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

prune298.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	10	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Merged error: 0.0b

Counts

132 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

2.0ms	(pow (cos x) 2)
2.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)

series73.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)
22.0ms	(pow (sin x) 2)
18.0ms	(pow (sin x) 2)

simplify64.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	146	308
1	487	260
2	1671	260
3	5001	256

prune238.0ms

Filtered

92 candidates to 56 candidates (60.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	92	10	102

Merged error: 0.0b

Counts

102 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.5b	(pow (* (tan x) (tan x)) 3)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1`
23×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
16×	`tan-quot`
13×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`pow-pow`
4×	`pow2` `expm1-log1p-u` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative` `unswap-sqr`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`

Counts

4 → 121

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
6.0ms	(pow (* (tan x) (tan x)) 3)

series163.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
65.0ms	(pow (* (tan x) (tan x)) 3)

simplify42.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	217	482
1	999	427
2	5001	410

prune343.0ms

Filtered

133 candidates to 74 candidates (55.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	133	10	143

Merged error: 0.0b

Counts

143 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
8.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series248.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))
94.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	373	1261
1	1240	1156
2	5001	1132

prune337.0ms

Filtered

143 candidates to 102 candidates (71.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	143	10	153

Merged error: 0.0b

Counts

153 → 10

regimes209.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms

sample902.0ms

Algorithm

intervals

Results

344.0ms	1441×	body	1280	valid
201.0ms	1263×	body	640	valid
152.0ms	4380×	body	80	valid
71.0ms	595×	body	320	valid
25.0ms	321×	body	160	valid