Details

sample281.0ms

Algorithm

intervals

Results

14.0ms	52×	body	1280	valid
6.0ms	35×	body	640	valid
5.0ms	140×	body	80	valid
3.0ms	23×	body	320	valid
0.0ms	6×	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

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: 0.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

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:

7.0ms	(/ (- 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))
8.0ms	(* (tan x) (tan x))

series231.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(- 1.0 (* (tan x) (tan x)))
34.0ms	(* (tan x) (tan x))
61.0ms	(* (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	918
2	5001	882

prune294.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	117	14	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	14	132

Merged error: 0.0b

Counts

132 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(- (sqrt 1.0) (tan x))
0.3b	(* (tan x) (tan x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
54×	`prod-diff`
50×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow1`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
6×	`fma-def` `fma-neg`
5×	`frac-times`
4×	`tan-quot` `expm1-log1p-u` `flip3--` `flip3-+` `flip--` `flip-+` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 163

Calls

4 calls:

13.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(+ (sqrt 1.0) (tan x))
6.0ms	(- (sqrt 1.0) (tan x))
8.0ms	(* (tan x) (tan x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
34.0ms	(+ (sqrt 1.0) (tan x))
41.0ms	(- (sqrt 1.0) (tan x))
34.0ms	(* (tan x) (tan x))

simplify74.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	550	2052
1	2400	1381
2	5001	1359

prune292.0ms

Filtered

175 candidates to 92 candidates (52.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	170	5	175
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	173	16	189

Merged error: 0.0b

Counts

189 → 16

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
11×	`pow1` `add-log-exp`
6×	`add-exp-log` `fma-def` `fma-neg` `add-cbrt-cube`
4×	`tan-quot` `expm1-log1p-u` `exp-prod` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`sum-log` `rem-exp-log` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `pow2` `frac-times` `sub-neg` `flip3--` `flip3-+` `pow-plus` `diff-log` `associate-r/` `exp-sum` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

5.0ms	(+ (sqrt 1.0) (tan x))
6.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))
6.0ms	(exp (+ (sqrt 1.0) (tan x)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (sqrt 1.0) (tan x))
40.0ms	(- (sqrt 1.0) (tan x))
33.0ms	(* (tan x) (tan x))
67.0ms	(exp (+ (sqrt 1.0) (tan x)))

simplify40.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	318	769
1	1061	553
2	5002	537

prune287.0ms

Filtered

119 candidates to 73 candidates (61.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	15	15
Picked	1	0	1
Done	0	0	0
Total	119	16	135

Merged error: 0.0b

Counts

135 → 16

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(- (tan x) (sqrt 1.0))
0.3b	(* (tan x) (tan x))
0.4b	(pow (tan x) 3)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
38×	`add-cube-cbrt`
36×	`prod-diff`
23×	`sqrt-prod`
12×	`pow1`
9×	`fma-neg`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`tan-quot`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `swap-sqr` `associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `pow-pow` `pow-plus` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`

Counts

4 → 135

Calls

4 calls:

6.0ms	(- (sqrt 1.0) (tan x))
7.0ms	(- (tan x) (sqrt 1.0))
5.0ms	(* (tan x) (tan x))
3.0ms	(pow (tan x) 3)

series166.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (sqrt 1.0) (tan x))
42.0ms	(- (tan x) (sqrt 1.0))
34.0ms	(* (tan x) (tan x))
52.0ms	(pow (tan x) 3)

simplify70.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	426	916
1	1882	694
2	5002	680

prune313.0ms

Filtered

147 candidates to 78 candidates (53.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	147	16	163

Merged error: 0.0b

Counts

163 → 16

regimes255.0ms

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	17	19
1	17	19

end0.0ms

sample942.0ms

Algorithm

intervals

Results

370.0ms	1478×	body	1280	valid
203.0ms	1255×	body	640	valid
157.0ms	4332×	body	80	valid
71.0ms	629×	body	320	valid
24.0ms	306×	body	160	valid