Details

sample99.0ms

Algorithm

intervals

Results

42.0ms	110×	body	1280	valid
19.0ms	69×	body	640	valid
11.0ms	256×	pre	80	true
4.0ms	29×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	7×	body	160	valid

simplify19.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
3.6b	(tan (+ y z))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sub-neg` `tan-sum` `associate-+r+` `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 → 42

Calls

3 calls:

6.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series289.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(+ x (- (tan (+ y z)) (tan a)))
114.0ms	(- (tan (+ y z)) (tan a))
55.0ms	(tan (+ y z))

simplify39.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	196	346
1	467	335
2	1316	334
3	5002	334

prune155.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.3b	(* (tan y) (tan z))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
2×	`+-commutative` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `flip3--` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

5.0ms	(+ (tan y) (tan z))
15.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
13.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))

series924.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (tan y) (tan z))
390.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
345.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
94.0ms	(* (tan y) (tan z))

simplify75.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	367	860
1	1074	821
2	3057	814
3	5001	814

prune294.0ms

Filtered

79 candidates to 60 candidates (75.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin z))
0.2b	(* (sin y) (sin z))
0.3b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
0.3b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

rewrite30.0ms

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×	`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 → 84

Calls

4 calls:

5.0ms	(* (sin y) (sin z))
5.0ms	(* (sin y) (sin z))
9.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
8.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin y) (sin z))
49.0ms	(* (sin y) (sin z))
100.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
102.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify37.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	247	756
1	1253	576
2	5001	576

prune435.0ms

Filtered

96 candidates to 62 candidates (64.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin y)) (cbrt (sin y)))
0.6b	(cbrt (sin y))
0.6b	(cbrt (sin y))
0.6b	(cbrt (sin y))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

7.0ms	(* (cbrt (sin y)) (cbrt (sin y)))
2.0ms	(cbrt (sin y))
2.0ms	(cbrt (sin y))
2.0ms	(cbrt (sin y))

series419.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (cbrt (sin y)) (cbrt (sin y)))
99.0ms	(cbrt (sin y))
106.0ms	(cbrt (sin y))
99.0ms	(cbrt (sin y))

simplify91.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	154	453
1	551	401
2	3082	369
3	5002	363

prune466.0ms

Filtered

85 candidates to 60 candidates (70.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes335.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	37
1	39	37

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	3974×	body	1280	valid
459.0ms	1985×	body	640	valid
329.0ms	8000×	pre	80	true
104.0ms	681×	body	320	valid
53.0ms	1089×	body	80	valid
29.0ms	271×	body	160	valid