Details

sample178.0ms

Algorithm

intervals

Results

104.0ms	139×	body	1280	valid
24.0ms	57×	body	640	valid
11.0ms	256×	pre	80	true
5.0ms	17×	body	320	valid
3.0ms	33×	body	80	valid
2.0ms	10×	body	160	valid

simplify24.0ms

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: 13.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.4b	(tan (+ y z))

rewrite45.0ms

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:

16.0ms	(+ x (- (tan (+ y z)) (tan a)))
18.0ms	(- (tan (+ y z)) (tan a))
8.0ms	(tan (+ y z))

series290.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(+ x (- (tan (+ y z)) (tan a)))
114.0ms	(- (tan (+ y z)) (tan a))
55.0ms	(tan (+ y z))

simplify94.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3128	507
3	5001	488

prune235.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
115×	`add-sqr-sqrt`
108×	`add-cube-cbrt` `prod-diff`
97×	`times-frac`
56×	`associate-+r+`
27×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
11×	`add-log-exp`
9×	`flip3--` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`tan-quot`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r-` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 227

Calls

4 calls:

28.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
148.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
96.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
18.0ms	(* (tan y) (tan z))

series1.1s

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
352.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
393.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
95.0ms	(* (tan y) (tan z))

simplify92.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	704	4490
1	2293	3769
2	5002	3667

prune741.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
2.3b	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

rewrite724.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 208

Calls

4 calls:

144.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
94.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
15.0ms	(* (tan y) (tan z))
459.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

series1.3s

Counts

4 → 12

Calls

4 calls:

359.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
392.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
98.0ms	(* (tan y) (tan z))
438.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

simplify77.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	641	4254
1	1986	3535
2	5002	3304

prune778.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin z))
0.2b	(* (sin y) (sin z))
0.2b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
0.2b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`pow1` `cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity` `div-exp`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `sin-mult` `add-log-exp`
2×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `-commutative` `div-inv` `associate-/l/` `associate-/l*` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

15.0ms	(* (sin y) (sin z))
12.0ms	(* (sin y) (sin z))
18.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
18.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin y) (sin z))
45.0ms	(* (sin y) (sin z))
100.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
102.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify42.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	253	800
1	1268	622
2	5001	622

prune458.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes392.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	30
1	36	30

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.1s	3936×	body	1280	valid
848.0ms	1932×	body	640	valid
333.0ms	8000×	pre	80	true
227.0ms	716×	body	320	valid
99.0ms	1126×	body	80	valid
60.0ms	290×	body	160	valid