Details

sample101.0ms

Algorithm

intervals

Results

48.0ms	118×	body	1280	valid
15.0ms	71×	body	640	valid
10.0ms	256×	pre	80	true
3.0ms	23×	body	320	valid
2.0ms	36×	body	80	valid
1.0ms	8×	body	160	valid

simplify20.0ms

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: 11.9b

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))
3.2b	(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))

series288.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(+ x (- (tan (+ y z)) (tan a)))
114.0ms	(- (tan (+ y z)) (tan a))
54.0ms	(tan (+ y z))

simplify40.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (13.0ms)

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

prune165.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

5.0ms	(+ (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
9.0ms	(* (tan y) (tan z))
15.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan y) (tan z))
92.0ms	(* (tan y) (tan z))
93.0ms	(* (tan y) (tan z))
471.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	542	1216
1	2440	1075
2	5002	1058

prune666.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
17×	`associate-*l/`
16×	`add-sqr-sqrt`
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`
2×	`frac-2neg` `flip3-+` `pow-prod-down` `frac-add` `clear-num` `associate-/r/` `*-commutative` `flip-+` `div-inv` `unswap-sqr`
1×	`frac-times` `div-sub` `associate-*r/`

Counts

4 → 94

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (sin z))
17.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))
6.0ms	(/ (* (tan y) (sin z)) (cos z))

series713.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (tan y) (tan z))
63.0ms	(* (tan y) (sin z))
465.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))
94.0ms	(/ (* (tan y) (sin z)) (cos z))

simplify81.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	631	1392
1	2964	1208
2	5001	1208

prune556.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log` `add-cbrt-cube`
21×	`times-frac`
20×	`add-sqr-sqrt`
18×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity` `div-exp` `prod-exp` `cbrt-unprod`
17×	`associate-*l/`
11×	`pow1`
10×	`associate-/l/`
7×	`swap-sqr` `associate-r` `associate-l` `associate-/r*` `div-inv`
6×	`tan-quot` `frac-sub`
5×	`flip3--` `flip--` `associate-/l*`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `frac-add` `associate-/r/` `flip-+`
1×	`pow2` `frac-times` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 132

Calls

4 calls:

6.0ms	(/ (* (tan y) (sin z)) (cos z))
6.0ms	(/ (* (tan y) (sin z)) (cos z))
23.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- (* 1 1) (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))) (cos a)))
13.0ms	(* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))

series834.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (* (tan y) (sin z)) (cos z))
98.0ms	(/ (* (tan y) (sin z)) (cos z))
518.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- (* 1 1) (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))) (cos a)))
121.0ms	(* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))

simplify120.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	824	2393
1	4573	1886
2	5002	1867

prune758.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes678.0ms

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	35	24
1	35	24

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.7s	3943×	body	1280	valid
452.0ms	1912×	body	640	valid
330.0ms	8000×	pre	80	true
113.0ms	717×	body	320	valid
55.0ms	1146×	body	80	valid
30.0ms	282×	body	160	valid