Details

sample201.0ms

Algorithm

intervals

Results

112.0ms	125×	body	1280	valid
31.0ms	63×	body	640	valid
20.0ms	256×	pre	80	true
7.0ms	22×	body	320	valid
4.0ms	35×	body	80	valid
3.0ms	11×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 13.1b

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)))
3.1b	(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:

15.0ms	(- (tan (+ y z)) (tan a))
8.0ms	(+ x (- (tan (+ y z)) (tan a)))
3.0ms	(tan (+ y z))

series341.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(- (tan (+ y z)) (tan a))
142.0ms	(+ x (- (tan (+ y z)) (tan a)))
59.0ms	(tan (+ y z))

simplify97.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (89.0ms)

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

prune490.0ms

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))

rewrite157.0ms

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:

11.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
78.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
50.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series1.1s

Counts

4 → 12

Calls

4 calls:

236.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
365.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
409.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
101.0ms	(* (tan y) (tan z))

simplify94.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (61.0ms)

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

prune786.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan y) (tan z)) (cos a))
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))
0.2b	(* (tan y) (tan z))

rewrite49.0ms

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:

12.0ms	(* (+ (tan y) (tan z)) (cos a))
21.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
8.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))

series918.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (+ (tan y) (tan z)) (cos a))
530.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
114.0ms	(* (tan y) (tan z))
103.0ms	(* (tan y) (tan z))

simplify89.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	607	1367
1	2828	1200
2	5002	1193

prune565.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

4.0ms	(/ (* (sin y) (cos a)) (cos y))
4.0ms	(* (sin z) (sin a))
4.0ms	(* (sin y) (sin z))
6.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (* (sin y) (cos a)) (cos y))
51.0ms	(* (sin z) (sin a))
45.0ms	(* (sin y) (sin z))
103.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify61.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	438	705
1	2210	568
2	5001	568

prune548.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes446.0ms

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	37	34
1	37	34

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.3s	3856×	body	1280	valid
1.0s	1962×	body	640	valid
663.0ms	8000×	pre	80	true
272.0ms	707×	body	320	valid
140.0ms	1150×	body	80	valid
86.0ms	325×	body	160	valid