Details

sample356.0ms

Algorithm

intervals

Results

21.0ms	48×	body	1280	valid
13.0ms	45×	body	640	valid
8.0ms	135×	body	80	valid
3.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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:

24.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series191.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
30.0ms	(* (tan x) (tan x))
41.0ms	(* (tan x) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (34.0ms)

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

prune281.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 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))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `log-pow`
18×	`exp-prod`
12×	`times-frac`
8×	`tan-quot` `add-exp-log` `add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`log-prod` `fma-neg` `prod-diff`
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` `unswap-sqr`
1×	`sub-neg` `log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `div-sub` `rem-log-exp` `flip--` `flip-+` `div-inv`

Counts

4 → 114

Calls

4 calls:

5.0ms	(- 1.0 (* (tan x) (tan x)))
14.0ms	(* (tan x) (tan x))
14.0ms	(* (tan x) (tan x))
27.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series175.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- 1.0 (* (tan x) (tan x)))
29.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
86.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify158.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 3 (149.0ms)

Iter	Nodes	Cost
0	313	858
1	968	771
2	4587	748
3	5001	743

prune302.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
39×	`add-cube-cbrt`
36×	`prod-diff`
22×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
10×	`log-pow`
9×	`exp-prod` `associate-r`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`fma-def` `add-log-exp`
5×	`frac-times` `flip3-+` `flip-+`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `flip3--` `times-frac` `associate-r/` `swap-sqr` `associate-l/` `flip--`
2×	`sub-neg` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `rem-log-exp` `sum-log` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--`

Counts

4 → 145

Calls

4 calls:

9.0ms	(+ (sqrt 1.0) (tan x))
57.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
17.0ms	(* (tan x) (tan x))
19.0ms	(log (exp (/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (sqrt 1.0) (tan x))
91.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
29.0ms	(* (tan x) (tan x))
173.0ms	(log (exp (/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify77.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	660	2001
1	2922	1442
2	5001	1415

prune351.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (fma (tan x) (tan x) 1.0))
0.2b	(/ (fma (tan x) (tan x) 1.0) (tan x))
0.3b	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
0.4b	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

1436×	`times-frac`
888×	`add-sqr-sqrt`
873×	`*-un-lft-identity`
867×	`add-cube-cbrt`
611×	`prod-diff`
107×	`div-inv`
58×	`associate-/r/`
45×	`tan-quot`
20×	`associate-/r*`
13×	`add-exp-log` `fma-neg` `add-cbrt-cube`
9×	`associate-/l*`
6×	`add-log-exp` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 783

Calls

4 calls:

5.0ms	(/ 1.0 (fma (tan x) (tan x) 1.0))
6.0ms	(/ (fma (tan x) (tan x) 1.0) (tan x))
13.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
74.0ms	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1.0 (fma (tan x) (tan x) 1.0))
74.0ms	(/ (fma (tan x) (tan x) 1.0) (tan x))
95.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
169.0ms	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

simplify306.0ms

Algorithm

egg-herbie

Counts

795 → 795

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2457	44315
1	5001	35123

prune2.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes138.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	13
1	13	13

end0.0ms

sample1.6s

Algorithm

intervals

Results

725.0ms	1596×	body	1280	valid
354.0ms	1259×	body	640	valid
241.0ms	4230×	body	80	valid
117.0ms	615×	body	320	valid
45.0ms	300×	body	160	valid