Details

sample113.0ms

Algorithm

intervals

Results

56.0ms	121×	body	1280	valid
15.0ms	66×	body	640	valid
11.0ms	256×	pre	80	true
3.0ms	22×	body	320	valid
2.0ms	36×	body	80	valid
1.0ms	11×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.1b	(+ x (- (tan (+ y z)) (tan a)))
2.4b	(tan (+ y z))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

8.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(+ x (- (tan (+ y z)) (tan a)))
4.0ms	(tan (+ y z))

series329.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(- (tan (+ y z)) (tan a))
136.0ms	(+ x (- (tan (+ y z)) (tan a)))
64.0ms	(tan (+ y z))

simplify101.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3057	507
3	5001	488

prune256.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `sum-log`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

6.0ms	(+ (tan y) (tan z))
20.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
19.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (tan y) (tan z))
389.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
442.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
111.0ms	(* (tan y) (tan z))

simplify82.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	676	4072
1	2087	3376
2	5001	3265

prune719.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (/ (+ (tan y) (tan z)) (- 1 (pow (* (tan y) (tan z)) 3))) (fma (fma (tan y) (tan z) 1) (* (tan y) (tan z)) 1) (+ (- (tan a)) x))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.3b	(pow (* (tan y) (tan z)) 3)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`tan-quot`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `frac-times` `pow-unpow` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod`
2×	`pow-pow` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `fma-udef` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

1.0ms	(fma (/ (+ (tan y) (tan z)) (- 1 (pow (* (tan y) (tan z)) 3))) (fma (fma (tan y) (tan z) 1) (* (tan y) (tan z)) 1) (+ (- (tan a)) x))
6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
7.0ms	(pow (* (tan y) (tan z)) 3)

series3.5s

Counts

4 → 12

Calls

4 calls:

3.2s	(fma (/ (+ (tan y) (tan z)) (- 1 (pow (* (tan y) (tan z)) 3))) (fma (fma (tan y) (tan z) 1) (* (tan y) (tan z)) 1) (+ (- (tan a)) x))
106.0ms	(* (tan y) (tan z))
106.0ms	(* (tan y) (tan z))
146.0ms	(pow (* (tan y) (tan z)) 3)

simplify74.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	427	933
1	2124	871
2	5001	870

prune570.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))
0.2b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
1.0ms	(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))
12.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series1.2s

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (tan y) (tan z))
106.0ms	(* (tan y) (tan z))
866.0ms	(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))
131.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	422	1108
1	1870	953
2	5002	930

prune444.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	29
1	27	29

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	3915×	body	1280	valid
447.0ms	1971×	body	640	valid
315.0ms	8000×	pre	80	true
107.0ms	689×	body	320	valid
51.0ms	1130×	body	80	valid
31.0ms	295×	body	160	valid