Details

sample215.0ms

Algorithm

intervals

Results

113.0ms	124×	body	1280	valid
32.0ms	62×	body	640	valid
26.0ms	256×	pre	80	true
9.0ms	23×	body	320	valid
6.0ms	37×	body	80	valid
3.0ms	10×	body	160	valid

simplify23.0ms

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: 12.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
4.2b	(tan (+ y z))

rewrite29.0ms

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:

13.0ms	(- (tan (+ y z)) (tan a))
9.0ms	(+ x (- (tan (+ y z)) (tan a)))
3.0ms	(tan (+ y z))

series319.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(- (tan (+ y z)) (tan a))
132.0ms	(+ x (- (tan (+ y z)) (tan a)))
58.0ms	(tan (+ y z))

simplify100.0ms

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

prune254.0ms

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

rewrite155.0ms

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:

3.0ms	(+ (tan y) (tan z))
52.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
82.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (tan y) (tan z))
432.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
374.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
103.0ms	(* (tan y) (tan z))

simplify85.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	676	4072
1	2087	3376
2	5001	3145

prune747.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(* (tan y) (tan z))
2.4b	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

rewrite404.0ms

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:

52.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
82.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))
252.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

series1.4s

Counts

4 → 12

Calls

4 calls:

422.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
372.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
103.0ms	(* (tan y) (tan z))
479.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

simplify80.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	641	4266
1	1986	3547
2	5002	3310

prune845.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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:

0.0ms	(fma (/ (+ (tan y) (tan z)) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (fma (tan y) (tan z) 1) (+ (- (tan a)) x))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
25.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series2.2s

Counts

4 → 12

Calls

4 calls:

1.9s	(fma (/ (+ (tan y) (tan z)) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (fma (tan y) (tan z) 1) (+ (- (tan a)) x))
100.0ms	(* (tan y) (tan z))
100.0ms	(* (tan y) (tan z))
126.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify56.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	419	1096
1	1863	946
2	5001	925

prune508.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes340.0ms

Accuracy

0% (0.2b 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	28	25
1	36	25
2	38	25
3	38	25

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.6s	3916×	body	1280	valid
1.1s	2051×	body	640	valid
775.0ms	8000×	pre	80	true
267.0ms	669×	body	320	valid
161.0ms	1080×	body	80	valid
84.0ms	284×	body	160	valid