Details

sample293.0ms

Algorithm

intervals

Results

13.0ms	51×	body	1280	valid
7.0ms	41×	body	640	valid
7.0ms	129×	body	80	valid
3.0ms	21×	body	320	valid
1.0ms	14×	body	160	valid

simplify17.0ms

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

prune4.0ms

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:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 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))

series222.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1.0 (* (tan x) (tan x)))
94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

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

prune269.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	11	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Merged error: 0.0b

Counts

132 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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:

7.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
8.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
7.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series248.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
93.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (33.0ms)

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

prune278.0ms

Filtered

143 candidates to 101 candidates (70.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	143	11	154

Merged error: 0.0b

Counts

154 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (cos 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:

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (sin x) 2)
18.0ms	(pow (sin x) 2)
16.0ms	(pow (cos x) 2)
17.0ms	(pow (cos 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	1669	260
3	5001	256

prune196.0ms

Filtered

92 candidates to 56 candidates (60.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	91	12	103

Merged error: 0.0b

Counts

103 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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:

5.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
10.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
6.0ms	(* (tan x) (tan x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
91.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify63.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	404	1182
1	1847	1018
2	5001	959

prune210.0ms

Filtered

152 candidates to 94 candidates (61.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	2	7	9
Picked	0	1	1
Done	1	1	2
Total	153	11	164

Merged error: 0.0b

Counts

164 → 11

regimes153.0ms

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	10	11
1	10	11

end0.0ms

sample960.0ms

Algorithm

intervals

Results

378.0ms	1509×	body	1280	valid
211.0ms	1244×	body	640	valid
158.0ms	4268×	body	80	valid
79.0ms	662×	body	320	valid
26.0ms	317×	body	160	valid

Details

sample293.0ms

simplify17.0ms

prune4.0ms

localize10.0ms

rewrite26.0ms

series222.0ms

simplify48.0ms

prune269.0ms

localize11.0ms

rewrite31.0ms

series248.0ms

simplify49.0ms

prune278.0ms

localize13.0ms

rewrite12.0ms

series73.0ms

simplify64.0ms

prune196.0ms

localize9.0ms

rewrite30.0ms

series209.0ms

simplify63.0ms

prune210.0ms

regimes153.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample960.0ms

Profiling