Details

sample183.0ms

Algorithm

intervals

Results

107.0ms	137×	body	1280	valid
29.0ms	65×	body	640	valid
10.0ms	256×	pre	80	true
4.0ms	15×	body	320	valid
3.0ms	30×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

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)))
3.0b	(tan (+ y z))

rewrite40.0ms

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:

17.0ms	(- (tan (+ y z)) (tan a))
15.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(tan (+ y z))

series257.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(- (tan (+ y z)) (tan a))
107.0ms	(+ x (- (tan (+ y z)) (tan a)))
48.0ms	(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

prune150.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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

rewrite259.0ms

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:

29.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
133.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
80.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
15.0ms	(* (tan y) (tan z))

series936.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
312.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
347.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
84.0ms	(* (tan y) (tan z))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	449	1259
1	1503	1211
2	5001	1204

prune351.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite691.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp`
3×	`associate-r` `associate-l`
2×	`sub-neg` `associate-+r+` `times-frac` `diff-log` `sum-log` `sin-mult` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`tan-quot` `+-commutative` `associate-+r-` `flip3--` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `-commutative` `frac-sub` `flip--` `flip-+` `div-inv` `associate-/l/` `associate-/l*` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

408.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a)))
250.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a))
18.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))
12.0ms	(* (sin y) (sin z))

series786.0ms

Counts

4 → 12

Calls

4 calls:

308.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a)))
349.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a))
88.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))
41.0ms	(* (sin y) (sin z))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	438	1203
1	1830	1082
2	5001	1082

prune372.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (/ (* (sin y) (sin z)) (* (cos y) (cos z))))
0.2b	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))
0.2b	(* (sin y) (sin z))
4.0b	(log (exp (/ (* (sin y) (sin z)) (* (cos y) (cos z)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
12×	`exp-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `log-pow`
5×	`prod-exp` `associate-/r/` `cos-mult` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `log-prod` `div-exp`
3×	`times-frac` `associate-r` `associate-l` `div-inv`
2×	`exp-lft-sqr` `sin-mult`
1×	`frac-2neg` `rem-log-exp` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `rem-exp-log` `associate-/l/` `associate-/l*` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

17.0ms	(exp (/ (* (sin y) (sin z)) (* (cos y) (cos z))))
18.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))
13.0ms	(* (sin y) (sin z))
17.0ms	(log (exp (/ (* (sin y) (sin z)) (* (cos y) (cos z)))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(exp (/ (* (sin y) (sin z)) (* (cos y) (cos z))))
88.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))
40.0ms	(* (sin y) (sin z))
89.0ms	(log (exp (/ (* (sin y) (sin z)) (* (cos y) (cos z)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	778
1	1410	646
2	5002	646

prune388.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes293.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	17
1	28	17

end0.0ms

sample5.0s

Algorithm

intervals

Results

3.0s	3888×	body	1280	valid
879.0ms	2005×	body	640	valid
320.0ms	8000×	pre	80	true
220.0ms	664×	body	320	valid
105.0ms	1173×	body	80	valid
59.0ms	270×	body	160	valid