Details

sample163.0ms

Algorithm

intervals

Results

82.0ms	113×	body	1280	valid
30.0ms	73×	body	640	valid
10.0ms	256×	pre	80	true
6.0ms	23×	body	320	valid
3.0ms	39×	body	80	valid
2.0ms	8×	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: 13.2b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite43.0ms

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:

18.0ms	(- (tan (+ y z)) (tan a))
17.0ms	(+ x (- (tan (+ y z)) (tan a)))
6.0ms	(tan (+ y z))

series340.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(- (tan (+ y z)) (tan a))
145.0ms	(+ x (- (tan (+ y z)) (tan a)))
61.0ms	(tan (+ y z))

simplify92.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (86.0ms)

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

prune232.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
0.2b	(* (+ (tan y) (tan z)) (cos a))
0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

19×	`associate-*l/`
18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`tan-quot` `*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
8×	`associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `times-frac` `pow-prod-down` `frac-add` `-commutative` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `associate-/r/`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out`

Counts

4 → 104

Calls

4 calls:

60.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
32.0ms	(* (+ (tan y) (tan z)) (cos a))
15.0ms	(* (tan y) (tan z))
15.0ms	(* (tan y) (tan z))

series942.0ms

Counts

4 → 12

Calls

4 calls:

556.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
172.0ms	(* (+ (tan y) (tan z)) (cos a))
105.0ms	(* (tan y) (tan z))
109.0ms	(* (tan y) (tan z))

simplify78.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	607	1365
1	2828	1198
2	5002	1191

prune529.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))
4.3b	(/ (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (- (tan y) (tan z)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

38×	`tan-quot`
24×	`add-sqr-sqrt`
20×	`associate-*l/`
18×	`*-un-lft-identity`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt`
11×	`associate-/l/`
10×	`frac-sub`
9×	`frac-times` `associate-r/` `associate-r` `associate-l*`
5×	`times-frac` `associate-/r*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l*`

Counts

4 → 117

Calls

4 calls:

15.0ms	(* (tan z) (tan z))
15.0ms	(* (tan y) (tan z))
15.0ms	(* (tan y) (tan z))
85.0ms	(/ (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (- (tan y) (tan z)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (tan z) (tan z))
105.0ms	(* (tan y) (tan z))
107.0ms	(* (tan y) (tan z))
367.0ms	(/ (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (- (tan y) (tan z)))

simplify64.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	468	1030
1	2253	919
2	5002	915

prune588.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan y) (tan z)) (cos a))
0.2b	(* (sin y) (sin z))
0.2b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
0.3b	(* (tan y) (tan z))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`pow1` `add-cube-cbrt` `associate-l`
9×	`associate-r`
7×	`prod-exp` `cbrt-unprod`
6×	`tan-quot`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `*-commutative` `unswap-sqr`
2×	`sin-mult`
1×	`frac-times` `frac-2neg` `flip3-+` `times-frac` `associate-r/` `frac-add` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `flip-+` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l*`

Counts

4 → 93

Calls

4 calls:

30.0ms	(* (+ (tan y) (tan z)) (cos a))
12.0ms	(* (sin y) (sin z))
20.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
15.0ms	(* (tan y) (tan z))

series439.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (+ (tan y) (tan z)) (cos a))
51.0ms	(* (sin y) (sin z))
114.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
102.0ms	(* (tan y) (tan z))

simplify53.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	433	725
1	2070	606
2	5002	606

prune515.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes466.0ms

Accuracy

0% (0.1b 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	29	28
1	29	28

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.0s	3901×	body	1280	valid
1.1s	1932×	body	640	valid
338.0ms	8000×	pre	80	true
220.0ms	725×	body	320	valid
100.0ms	1158×	body	80	valid
56.0ms	284×	body	160	valid