Details

sample211.0ms

Algorithm

intervals

Results

103.0ms	113×	body	1280	valid
45.0ms	75×	body	640	valid
29.0ms	256×	pre	80	true
8.0ms	22×	body	320	valid
4.0ms	37×	body	80	valid
2.0ms	9×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
5.7b	(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	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series104.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ x (- (tan (+ y z)) (tan a)))
40.0ms	(- (tan (+ y z)) (tan a))
18.0ms	(tan (+ y z))

simplify36.0ms

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

prune393.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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)))
0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))

rewrite47.0ms

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:

12.0ms	(* (+ (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))

series261.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (+ (tan y) (tan z)) (cos a))
175.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
23.0ms	(* (tan y) (tan z))
25.0ms	(* (tan y) (tan z))

simplify69.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (58.0ms)

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

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))
0.3b	(pow (* (tan y) (tan z)) 3)
28.8b	(cbrt (pow (* (tan y) (tan z)) 3))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`tan-quot`
14×	`add-sqr-sqrt`
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×	`frac-times` `associate-r/` `associate-l/` `add-log-exp`
3×	`pow-unpow` `cbrt-div` `pow-prod-down` `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 → 87

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
6.0ms	(pow (* (tan y) (tan z)) 3)
3.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

series112.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (tan y) (tan z))
25.0ms	(* (tan y) (tan z))
41.0ms	(pow (* (tan y) (tan z)) 3)
23.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	263	510
1	1337	490
2	5002	489

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

108×	`associate-*l/`
84×	`pow1`
73×	`frac-times`
68×	`tan-quot`
51×	`associate-*r/`
48×	`add-exp-log` `add-cbrt-cube`
42×	`associate-/l/`
40×	`frac-sub`
35×	`pow-prod-down`
30×	`flip3-+` `flip-+`
27×	`cos-mult`
25×	`prod-exp` `cbrt-unprod`
19×	`flip3--` `flip--`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity` `pow-sqr` `pow-prod-up`
5×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `associate-/r/`
4×	`pow-plus` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`pow2` `swap-sqr`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`

Counts

4 → 194

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
23.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
21.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
86.0ms	(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (cos y) (cos z)) (* (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (cos a))))

series539.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (tan y) (tan z))
34.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
34.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
446.0ms	(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (cos y) (cos z)) (* (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (cos a))))

simplify65.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1335	4881
1	5002	4507

prune4.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes1.8s

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	30	22
1	30	22

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.5s	3876×	body	1280	valid
1.1s	1968×	body	640	valid
940.0ms	8000×	pre	80	true
264.0ms	689×	body	320	valid
139.0ms	1165×	body	80	valid
79.0ms	302×	body	160	valid