Details

analyze3.4s

Algorithm

sampling

Space saved by range analysis: 99.761164%

Space saved by search: 99.761164%

Guaranteed chance to sample good point: 12.109375%

sample113.0ms

Algorithm

intervals

Results

53.0ms	132×	body	1280	valid
18.0ms	256×	pre	80	true
17.0ms	47×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	43×	body	80	valid
1.0ms	8×	body	160	valid

simplify385.0ms

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

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: 10.6b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
1.9b	(tan (+ y z))

rewrite20.0ms

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:

5.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series111.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ x (- (tan (+ y z)) (tan a)))
46.0ms	(- (tan (+ y z)) (tan a))
25.0ms	(tan (+ y z))

simplify37.0ms

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

prune103.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	42	9	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	9	52

Merged error: 0.0b

Counts

52 → 9

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))

rewrite42.0ms

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:

8.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
15.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
12.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series323.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
127.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
119.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
22.0ms	(* (tan y) (tan z))

simplify114.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	449	1261
1	1503	1213
2	4992	1204
3	5001	1204

prune165.0ms

Filtered

75 candidates to 102 candidates (-36.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	102	9	111

Merged error: 0.0b

Counts

111 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (cbrt (pow (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) 3)) (tan a))
0.2b	(* (tan y) (tan z))
0.5b	(pow (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) 3)
7.4b	(cbrt (pow (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) 3))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
50×	`times-frac`
48×	`cbrt-prod`
40×	`add-cube-cbrt`
38×	`unpow-prod-down` `cube-prod`
12×	`distribute-lft-out`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
7×	`pow1` `difference-of-squares`
6×	`add-log-exp`
5×	`tan-quot` `flip3--` `flip--`
4×	`div-inv`
3×	`cube-div` `pow-unpow` `associate-r` `associate-l` `sqr-pow`
2×	`cube-mult` `cbrt-div` `unpow3` `pow-exp` `rem-cube-cbrt`
1×	`cbrt-undiv` `frac-times` `pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 150

Calls

4 calls:

21.0ms	(- (cbrt (pow (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) 3)) (tan a))
5.0ms	(* (tan y) (tan z))
9.0ms	(pow (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) 3)
9.0ms	(cbrt (pow (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) 3))

series276.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (cbrt (pow (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) 3)) (tan a))
21.0ms	(* (tan y) (tan z))
81.0ms	(pow (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) 3)
55.0ms	(cbrt (pow (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	619	2452
1	2602	2256
2	5001	2247

prune180.0ms

Filtered

84 candidates to 162 candidates (-92.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	162	9	171

Merged error: 0.0b

Counts

171 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.3b	(* (tan a) (tan a))
0.4b	(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
1.3b	(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
80×	`times-frac`
72×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
27×	`swap-sqr`
24×	`associate-r` `associate-l`
23×	`distribute-lft-out`
22×	`add-exp-log` `add-cbrt-cube`
21×	`tan-quot`
20×	`pow1`
11×	`associate-/r/` `associate-/l/`
9×	`frac-times` `associate-r/` `associate-l/` `frac-sub`
6×	`prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `div-inv` `difference-of-squares`
4×	`associate-/r` `associate-/l` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`frac-2neg` `flip3-+` `div-sub` `frac-add` `clear-num` `flip-+`

Counts

4 → 188

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan a) (tan a))
20.0ms	(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
32.0ms	(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (tan y) (tan z))
9.0ms	(* (tan a) (tan a))
67.0ms	(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
451.0ms	(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	986	4500
1	5001	4174

prune258.0ms

Filtered

128 candidates to 200 candidates (-56.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	200	9	209

Merged error: 0.0b

Counts

209 → 9

regimes1.1s

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	22	13
1	22	13

end0.0ms

analyze3.2s

Algorithm

sampling

Space saved by range analysis: 99.761164%

Space saved by search: 99.761164%

Guaranteed chance to sample good point: 12.109375%

sample3.2s

Algorithm

intervals

Results

1.7s	3962×	body	1280	valid
544.0ms	8000×	pre	80	true
472.0ms	1931×	body	640	valid
122.0ms	710×	body	320	valid
57.0ms	1089×	body	80	valid
38.0ms	308×	body	160	valid

Details

analyze3.4s

sample113.0ms

simplify385.0ms

prune6.0ms

localize13.0ms

rewrite20.0ms

series111.0ms

simplify37.0ms

prune103.0ms

localize16.0ms

rewrite42.0ms

series323.0ms

simplify114.0ms

prune165.0ms

localize19.0ms

rewrite53.0ms

series276.0ms

simplify80.0ms

prune180.0ms

localize22.0ms

rewrite70.0ms

series547.0ms

simplify57.0ms

prune258.0ms

regimes1.1s

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze3.2s

sample3.2s

Profiling