Details

sample281.0ms

Algorithm

intervals

Results

13.0ms	53×	body	1280	valid
6.0ms	38×	body	640	valid
6.0ms	144×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	8×	body	160	valid

simplify15.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

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))))
0.3b	(* (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))
8.0ms	(* (tan x) (tan x))

series214.0ms

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))))
32.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

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

prune281.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cbrt (pow (tan x) 6))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.6b	(pow (tan x) 6)
10.5b	(cbrt (pow (tan x) 6))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
25×	`add-cube-cbrt`
24×	`times-frac`
19×	`cbrt-prod`
16×	`difference-of-squares`
12×	`pow1`
10×	`unpow-prod-down`
9×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
6×	`sqr-pow`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l` `associate-/r*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `pow-plus` `pow1/3` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

12.0ms	(/ (- 1.0 (cbrt (pow (tan x) 6))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
3.0ms	(pow (tan x) 6)
3.0ms	(cbrt (pow (tan x) 6))

series222.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (cbrt (pow (tan x) 6))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(* (tan x) (tan x))
59.0ms	(pow (tan x) 6)
35.0ms	(cbrt (pow (tan x) 6))

simplify58.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	473	1218
1	1687	1100
2	5001	1065

prune346.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (tan x) 6)
0.6b	(pow (tan x) 6)
10.5b	(cbrt (pow (tan x) 6))
10.5b	(cbrt (pow (tan x) 6))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `pow-unpow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow (tan x) 6)
3.0ms	(pow (tan x) 6)
2.0ms	(cbrt (pow (tan x) 6))
3.0ms	(cbrt (pow (tan x) 6))

series196.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (tan x) 6)
64.0ms	(pow (tan x) 6)
32.0ms	(cbrt (pow (tan x) 6))
36.0ms	(cbrt (pow (tan x) 6))

simplify102.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	147	396
1	486	350
2	2205	340
3	5001	306

prune238.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma 1.0 1.0 (* (- (pow (tan x) 3)) (tan x))) (fma (tan x) (tan x) 1.0))
0.2b	(* (- (pow (tan x) 3)) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(pow (tan x) 3)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `associate-l`
27×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
9×	`tan-quot` `unpow-prod-down` `times-frac` `cube-prod`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `cube-mult` `pow-unpow` `unpow3` `swap-sqr` `associate-/r` `associate-/l` `sqr-pow`
2×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-neg-frac` `unswap-sqr`
1×	`cbrt-undiv` `distribute-lft-neg-out` `pow2` `pow-to-exp` `neg-mul-1` `pow-pow` `frac-2neg` `pow-plus` `div-exp` `pow-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `rem-cube-cbrt`

Counts

4 → 134

Calls

4 calls:

3.0ms	(/ (fma 1.0 1.0 (* (- (pow (tan x) 3)) (tan x))) (fma (tan x) (tan x) 1.0))
9.0ms	(* (- (pow (tan x) 3)) (tan x))
5.0ms	(* (tan x) (tan x))
3.0ms	(pow (tan x) 3)

series289.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (fma 1.0 1.0 (* (- (pow (tan x) 3)) (tan x))) (fma (tan x) (tan x) 1.0))
68.0ms	(* (- (pow (tan x) 3)) (tan x))
32.0ms	(* (tan x) (tan x))
51.0ms	(pow (tan x) 3)

simplify102.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	457	970
1	2546	876
2	5001	853

prune412.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes160.0ms

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	10	9
1	10	9

end0.0ms

sample948.0ms

Algorithm

intervals

Results

381.0ms	1505×	body	1280	valid
207.0ms	1280×	body	640	valid
151.0ms	4280×	body	80	valid
70.0ms	618×	body	320	valid
25.0ms	317×	body	160	valid