Details

sample167.0ms

Algorithm

intervals

Results

93.0ms	121×	body	1280	valid
29.0ms	65×	body	640	valid
10.0ms	256×	pre	80	true
5.0ms	16×	body	320	valid
4.0ms	42×	body	80	valid
2.0ms	12×	body	160	valid

simplify28.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

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)))
2.6b	(tan (+ y z))

rewrite19.0ms

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:

7.0ms	(- (tan (+ y z)) (tan a))
8.0ms	(+ x (- (tan (+ y z)) (tan a)))
3.0ms	(tan (+ y z))

series279.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(- (tan (+ y z)) (tan a))
120.0ms	(+ x (- (tan (+ y z)) (tan a)))
49.0ms	(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

prune146.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (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))

rewrite48.0ms

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×	`prod-exp` `cbrt-unprod` `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 → 96

Calls

4 calls:

13.0ms	(* (+ (tan y) (tan z)) (cos a))
22.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))

series793.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (+ (tan y) (tan z)) (cos a))
468.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
90.0ms	(* (tan y) (tan z))
90.0ms	(* (tan y) (tan z))

simplify73.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	587	1304
1	2694	1144
2	5001	1128

prune478.0ms

Filtered

108 candidates to 83 candidates (76.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

4.0ms	(/ (* (sin y) (tan z)) (cos y))
25.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (sin y) (tan z))

series746.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (* (sin y) (tan z)) (cos y))
474.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
91.0ms	(* (tan y) (tan z))
78.0ms	(* (sin y) (tan z))

simplify82.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	632	1390
1	3029	1206
2	5001	1206

prune534.0ms

Filtered

106 candidates to 81 candidates (76.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (sin y) (tan z))
0.3b	(pow (* (tan y) (tan z)) 3)
25.0b	(cbrt (pow (* (tan y) (tan z)) 3))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`tan-quot`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-prod`
6×	`cube-div` `associate-r` `associate-l`
4×	`associate-*r/` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `rem-cbrt-cube`

Counts

4 → 85

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
4.0ms	(* (sin y) (tan z))
4.0ms	(pow (* (tan y) (tan z)) 3)
3.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

series380.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (tan y) (tan z))
78.0ms	(* (sin y) (tan z))
120.0ms	(pow (* (tan y) (tan z)) 3)
90.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	315	501
1	1578	480
2	5001	479

prune469.0ms

Filtered

97 candidates to 69 candidates (71.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes493.0ms

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	35	24
1	35	24

end0.0ms

sample4.9s

Algorithm

intervals

Results

3.0s	3953×	body	1280	valid
880.0ms	1932×	body	640	valid
311.0ms	8000×	pre	80	true
205.0ms	710×	body	320	valid
99.0ms	1137×	body	80	valid
60.0ms	268×	body	160	valid