Details

sample282.0ms

Algorithm

intervals

Results

14.0ms	49×	body	1280	valid
7.0ms	40×	body	640	valid
5.0ms	136×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	13×	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

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:

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

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))

series225.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
97.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (37.0ms)

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

prune298.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	116	15	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	15	132

Merged error: 0.0b

Counts

132 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
21×	`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`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`associate-/r*`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `log1p-udef` `flip3--` `frac-2neg` `flip3-+` `div-sub` `log1p-expm1` `div-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 109

Calls

4 calls:

9.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
1.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

series385.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))
220.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	366	1025
1	1339	934
2	5002	895

prune284.0ms

Filtered

121 candidates to 83 candidates (68.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	122	14	136

Merged error: 0.0b

Counts

136 → 14

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

4.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
11.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
96.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
37.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))

simplify65.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (49.0ms)

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

prune267.0ms

Filtered

152 candidates to 95 candidates (62.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	154	12	166

Merged error: 0.0b

Counts

166 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
42×	`add-cube-cbrt`
37×	`times-frac`
23×	`sqrt-prod`
22×	`associate-r`
18×	`prod-diff`
16×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--` `add-log-exp`
6×	`pow1` `fma-def` `fma-neg` `associate-/l*`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 153

Calls

4 calls:

5.0ms	(+ (sqrt 1.0) (tan x))
14.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
9.0ms	(- (sqrt 1.0) (tan x))
8.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

series394.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (sqrt 1.0) (tan x))
217.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
37.0ms	(- (sqrt 1.0) (tan x))
107.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	539	1883
1	2443	1567
2	5002	1538

prune317.0ms

Filtered

165 candidates to 112 candidates (67.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	165	12	177

Merged error: 0.0b

Counts

177 → 12

regimes222.0ms

Accuracy

0% (0.4b 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	12	15
1	12	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

408.0ms	1558×	body	1280	valid
210.0ms	1238×	body	640	valid
163.0ms	4225×	body	80	valid
77.0ms	642×	body	320	valid
29.0ms	337×	body	160	valid