Details

sample504.0ms

Algorithm

intervals

Results

142.0ms	53×	body	2560	valid
48.0ms	83×	body	1280	valid
19.0ms	69×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	9×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

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: 34.1b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (tan x))
1.4b	(- x (sin x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series176.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
60.0ms	(- x (tan x))
40.0ms	(- x (sin x))

simplify150.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	684
2	4781	684
3	5001	684

prune176.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
14.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series105.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 27/2800 (pow x 4))
24.0ms	(* 9/40 (pow x 2))
46.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify43.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	316
2	5001	313

prune128.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	75	4	79

Merged error: 0.0b

Counts

79 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
1.6b	(log (exp (* 9/40 (pow x 2))))
18.0b	(- (log (exp (* 9/40 (pow x 2)))) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
15×	`-un-lft-identity` `associate-r*`
14×	`add-exp-log`
12×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
7×	`unswap-sqr`
6×	`pow1` `log-prod` `associate-l` `prod-exp`
4×	`log-pow` `sqr-pow`
3×	`associate--l+`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unpow2`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `sum-log` `flip--` `associate--r+` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

5.0ms	(* 27/2800 (pow x 4))
8.0ms	(* 9/40 (pow x 2))
2.0ms	(log (exp (* 9/40 (pow x 2))))
7.0ms	(- (log (exp (* 9/40 (pow x 2)))) (+ (* 27/2800 (pow x 4)) 1/2))

series129.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 27/2800 (pow x 4))
27.0ms	(* 9/40 (pow x 2))
24.0ms	(log (exp (* 9/40 (pow x 2))))
43.0ms	(- (log (exp (* 9/40 (pow x 2)))) (+ (* 27/2800 (pow x 4)) 1/2))

simplify45.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	306	499
1	1175	434
2	5002	434

prune195.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	98	4	102

Merged error: 0.0b

Counts

102 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
22.6b	(- (* 81/1600 (pow x 4)) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ (* 27/2800 (pow x 4)) 1/2)))
26.1b	(/ (- (* 81/1600 (pow x 4)) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ (* 27/2800 (pow x 4)) 1/2))) (+ (+ (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
12×	`times-frac`
10×	`add-cbrt-cube`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp` `add-log-exp`
4×	`pow1` `associate-/r*` `distribute-lft-out` `sqr-pow`
3×	`associate-/l*`
2×	`pow-to-exp` `flip3--` `pow-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `associate--r+` `unpow2`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
4.0ms	(- (* 81/1600 (pow x 4)) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ (* 27/2800 (pow x 4)) 1/2)))
14.0ms	(/ (- (* 81/1600 (pow x 4)) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ (* 27/2800 (pow x 4)) 1/2))) (+ (+ (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2))

series259.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 27/2800 (pow x 4))
26.0ms	(* 9/40 (pow x 2))
102.0ms	(- (* 81/1600 (pow x 4)) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ (* 27/2800 (pow x 4)) 1/2)))
96.0ms	(/ (- (* 81/1600 (pow x 4)) (* (+ (* 27/2800 (pow x 4)) 1/2) (+ (* 27/2800 (pow x 4)) 1/2))) (+ (+ (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2))

simplify82.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	476	1400
1	2376	1276
2	5001	1273

prune248.0ms

Filtered

114 candidates to 76 candidates (66.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	114	4	118

Merged error: 0.0b

Counts

118 → 4

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.0b

bsearch89.0ms

Steps

Iters	Range		Point
9	2.8262556577633816e-09	1.3569245790634763	0.030020902626644374
7	-5.155753157609302	-0.022529268385055725	-0.030671364754495358

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	59
1	45	59

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.9s	1583×	body	2560	valid
1.6s	2814×	body	1280	valid
514.0ms	1927×	body	640	valid
157.0ms	901×	body	320	valid
56.0ms	450×	body	160	valid
25.0ms	325×	body	80	valid

Details

sample504.0ms

simplify12.0ms

prune4.0ms

localize11.0ms

rewrite21.0ms

series176.0ms

simplify150.0ms

prune176.0ms

localize10.0ms

rewrite19.0ms

series105.0ms

simplify43.0ms

prune128.0ms

localize11.0ms

rewrite25.0ms

series129.0ms

simplify45.0ms

prune195.0ms

localize15.0ms

rewrite31.0ms

series259.0ms

simplify82.0ms

prune248.0ms

regimes34.0ms

bsearch89.0ms

simplify2.0ms

end0.0ms

sample6.4s

Profiling