Details

sample103.0ms

Algorithm

intervals

Results

50.0ms	125×	body	1280	valid
14.0ms	65×	body	640	valid
10.0ms	256×	pre	80	true
2.0ms	15×	body	320	valid
2.0ms	43×	body	80	valid
1.0ms	8×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
3.8b	(tan (+ y z))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `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 → 72

Calls

3 calls:

14.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(+ x (- (tan (+ y z)) (tan a)))
4.0ms	(tan (+ y z))

series318.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(- (tan (+ y z)) (tan a))
133.0ms	(+ x (- (tan (+ y z)) (tan a)))
56.0ms	(tan (+ y z))

simplify97.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3057	507
3	5001	488

prune230.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Merged error: 0.1b

Counts

82 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `sum-log`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

5.0ms	(+ (tan y) (tan z))
15.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
23.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
6.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (tan y) (tan z))
432.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
379.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
104.0ms	(* (tan y) (tan z))

simplify88.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	676	4072
1	2087	3376
2	5001	3145

prune661.0ms

Filtered

219 candidates to 132 candidates (60.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	209	10	219
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	216	11	227

Merged error: 0.0b

Counts

227 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan y) (tan z)) (cos a))
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)))

rewrite39.0ms

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×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 104

Calls

4 calls:

8.0ms	(* (+ (tan y) (tan z)) (cos a))
6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
17.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series929.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (+ (tan y) (tan z)) (cos a))
106.0ms	(* (tan y) (tan z))
107.0ms	(* (tan y) (tan z))
544.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify82.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	607	1365
1	2835	1198
2	5001	1191

prune716.0ms

Filtered

116 candidates to 91 candidates (78.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	116	11	127

Merged error: 0.0b

Counts

127 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ x (cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)))
0.2b	(* (tan y) (tan z))
0.7b	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
2.7b	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
18×	`cbrt-prod`
13×	`add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod`
8×	`difference-of-squares`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`tan-quot` `cube-div` `add-log-exp`
4×	`expm1-log1p-u` `times-frac` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-unpow` `cbrt-div` `fma-def` `associate-r` `associate-l`
2×	`cube-mult` `flip3--` `unpow3` `frac-sub` `flip--` `sqr-pow`
1×	`+-commutative` `frac-times` `pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `sum-log` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `flip-+` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

18.0ms	(+ x (cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)))
6.0ms	(* (tan y) (tan z))
14.0ms	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
15.0ms	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

series1.6s

Counts

4 → 12

Calls

4 calls:

384.0ms	(+ x (cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)))
106.0ms	(* (tan y) (tan z))
693.0ms	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
422.0ms	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	489	1822
1	1921	1689
2	5001	1681

prune352.0ms

Filtered

118 candidates to 78 candidates (66.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	118	11	129

Merged error: 0.0b

Counts

129 → 11

regimes399.0ms

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	26	20
1	26	20

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	3900×	body	1280	valid
461.0ms	2016×	body	640	valid
325.0ms	8000×	pre	80	true
103.0ms	665×	body	320	valid
58.0ms	1150×	body	80	valid
29.0ms	269×	body	160	valid

Details

sample103.0ms

simplify27.0ms

prune3.0ms

localize11.0ms

rewrite28.0ms

series318.0ms

simplify97.0ms

prune230.0ms

localize17.0ms

rewrite61.0ms

series1.0s

simplify88.0ms

prune661.0ms

localize29.0ms

rewrite39.0ms

series929.0ms

simplify82.0ms

prune716.0ms

localize21.0ms

rewrite56.0ms

series1.6s

simplify80.0ms

prune352.0ms

regimes399.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.9s

Profiling