Details

sample185.0ms

Algorithm

intervals

Results

109.0ms	133×	body	1280	valid
29.0ms	62×	body	640	valid
11.0ms	256×	pre	80	true
7.0ms	20×	body	320	valid
3.0ms	29×	body	80	valid
3.0ms	12×	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: 13.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.4b	(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)))
8.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series288.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(+ x (- (tan (+ y z)) (tan a)))
112.0ms	(- (tan (+ y z)) (tan a))
58.0ms	(tan (+ y z))

simplify41.0ms

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

prune161.0ms

Pruning

9 alts after pruning (9 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))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`tan-quot`
6×	`pow1` `distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `associate-+r+` `flip3--` `flip3-+` `diff-log` `sum-log` `associate-/r/` `flip--` `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` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

11.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
70.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
42.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
332.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
379.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
91.0ms	(* (tan y) (tan z))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	449	1261
1	1503	1213
2	5001	1205

prune353.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan y))
0.3b	(* (tan z) (tan z))
3.1b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

42×	`tan-quot`
22×	`add-sqr-sqrt`
20×	`pow1`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `frac-times` `add-cbrt-cube`
12×	`associate-*r/` `frac-sub`
11×	`associate-*l/` `associate-/r/` `associate-/l/`
9×	`associate-r` `associate-l`
8×	`flip3--` `flip--`
6×	`swap-sqr`
4×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
3×	`pow-prod-down` `*-commutative` `unswap-sqr`
2×	`cbrt-undiv` `pow2` `pow-plus` `div-exp` `pow-sqr` `pow-prod-up` `difference-of-squares`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 123

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan y))
5.0ms	(* (tan z) (tan z))
23.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan y) (tan z))
37.0ms	(* (tan y) (tan y))
32.0ms	(* (tan z) (tan z))
350.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))

simplify85.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	605	1299
1	2965	1134
2	5001	1063

prune528.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

24.0ms	(/ (- (* (+ (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))
11.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))

series960.0ms

Counts

4 → 12

Calls

4 calls:

476.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
94.0ms	(* (tan y) (tan z))
93.0ms	(* (tan y) (tan z))
297.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))

simplify93.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	655	1681
1	3094	1507
2	5002	1490

prune460.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes333.0ms

Accuracy

0% (0.2b 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	36	24
1	36	24

end0.0ms

sample5.0s

Algorithm

intervals

Results

3.1s	3957×	body	1280	valid
901.0ms	1985×	body	640	valid
359.0ms	8000×	pre	80	true
206.0ms	657×	body	320	valid
102.0ms	1113×	body	80	valid
64.0ms	288×	body	160	valid