Details

analyze16.6s

Algorithm: search

sample127.0ms

Algorithm

intervals

Results

70.0ms	123×	body	1280	valid
18.0ms	256×	pre	80	true
15.0ms	61×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	40×	body	80	valid
1.0ms	7×	body	160	valid

simplify368.0ms

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: 12.4b

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))
2.1b	(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:

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

series119.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ x (- (tan (+ y z)) (tan a)))
33.0ms	(- (tan (+ y z)) (tan a))
45.0ms	(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

prune113.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	41	10	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	10	52

Merged error: 0.1b

Counts

52 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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))))
12.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series334.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
131.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
123.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
22.0ms	(* (tan y) (tan z))

simplify117.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	449	1259
1	1503	1211
2	4992	1203
3	5001	1203

prune171.0ms

Filtered

75 candidates to 102 candidates (-36.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	7	102
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	101	11	112

Merged error: 0.1b

Counts

112 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
5.5b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))

rewrite38.0ms

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 z) (tan z))
7.0ms	(* (tan y) (tan y))
17.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))

series144.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (tan y) (tan z))
9.0ms	(* (tan z) (tan z))
9.0ms	(* (tan y) (tan y))
105.0ms	(/ (- (* (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

prune176.0ms

Filtered

93 candidates to 135 candidates (-45.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	135	11	146

Merged error: 0.1b

Counts

146 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan y) (tan z)) 3)))) (tan a))
0.2b	(* (tan y) (tan z))
0.3b	(pow (* (tan y) (tan z)) 3)
29.0b	(cbrt (pow (* (tan y) (tan z)) 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`tan-quot`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`cube-div` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

22.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan y) (tan z)) 3)))) (tan a))
5.0ms	(* (tan y) (tan z))
5.0ms	(pow (* (tan y) (tan z)) 3)
4.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

series201.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan y) (tan z)) 3)))) (tan a))
22.0ms	(* (tan y) (tan z))
36.0ms	(pow (* (tan y) (tan z)) 3)
25.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	377	783
1	1645	739
2	5001	738

prune124.0ms

Filtered

69 candidates to 94 candidates (-36.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	94	11	105

Merged error: 0.1b

Counts

105 → 11

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	23	19
1	23	19

end0.0ms

analyze15.8s

Algorithm: search

sample3.1s

Algorithm

intervals

Results

1.6s	3989×	body	1280	valid
516.0ms	8000×	pre	80	true
460.0ms	1998×	body	640	valid
105.0ms	666×	body	320	valid
51.0ms	1084×	body	80	valid
28.0ms	263×	body	160	valid

Details

analyze16.6s

sample127.0ms

simplify368.0ms

prune6.0ms

localize13.0ms

rewrite20.0ms

series119.0ms

simplify37.0ms

prune113.0ms

localize18.0ms

rewrite39.0ms

series334.0ms

simplify117.0ms

prune171.0ms

localize19.0ms

rewrite38.0ms

series144.0ms

simplify85.0ms

prune176.0ms

localize19.0ms

rewrite38.0ms

series201.0ms

simplify51.0ms

prune124.0ms

regimes1.1s

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze15.8s

sample3.1s

Profiling