Details

sample464.0ms

Algorithm

intervals

Results

127.0ms	48×	body	2560	valid
51.0ms	86×	body	1280	valid
17.0ms	64×	body	640	valid
6.0ms	36×	body	320	valid
3.0ms	14×	body	80	valid
1.0ms	8×	body	160	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 (100.0%)

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: 34.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (sin x))
1.1b	(- x (tan x))

rewrite36.0ms

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)))
4.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series177.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
63.0ms	(- x (tan x))

simplify147.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	360	718
1	1133	685
2	4726	685
3	5003	685

prune164.0ms

Filtered

89 candidates to 63 candidates (29.2%)

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))
0.1b	(* 9/40 (pow x 2))
14.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

6.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
25.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series110.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 27/2800 (pow x 4))
28.0ms	(* 9/40 (pow x 2))
46.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	293	472
1	1125	437
2	5002	436

prune127.0ms

Filtered

89 candidates to 50 candidates (43.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	88	5	93

Merged error: 0.0b

Counts

93 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
0.9b	(log (exp (* 27/2800 (pow x 4))))
14.8b	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

6.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
8.0ms	(log (exp (* 27/2800 (pow x 4))))
26.0ms	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

series146.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 27/2800 (pow x 4))
24.0ms	(* 9/40 (pow x 2))
39.0ms	(log (exp (* 27/2800 (pow x 4))))
45.0ms	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

simplify47.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	381	670
1	1331	604
2	5001	599

prune213.0ms

Filtered

128 candidates to 76 candidates (40.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	128	5	133

Merged error: 0.0b

Counts

133 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.9b	(log (sqrt (exp (* 27/2800 (pow x 4)))))
0.9b	(log (sqrt (exp (* 27/2800 (pow x 4)))))
14.8b	(- (* 9/40 (pow x 2)) (log (sqrt (exp (* 27/2800 (pow x 4))))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
46×	`log-pow`
40×	`sqrt-pow1`
36×	`exp-prod`
27×	`*-un-lft-identity`
22×	`associate-r`
21×	`add-cube-cbrt`
18×	`log-prod`
14×	`unswap-sqr`
13×	`unpow-prod-down`
12×	`pow1`
11×	`add-exp-log` `associate-l`
9×	`sqrt-prod` `add-log-exp`
7×	`sqr-pow`
6×	`add-cbrt-cube` `associate--r+`
5×	`difference-of-squares`
4×	`distribute-lft-out--`
3×	`prod-exp` `*-commutative` `unpow2`
2×	`exp-to-pow` `pow1/2` `diff-log` `rem-log-exp`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-prod-down` `pow-exp` `flip--` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

6.0ms	(* 9/40 (pow x 2))
8.0ms	(log (sqrt (exp (* 27/2800 (pow x 4)))))
7.0ms	(log (sqrt (exp (* 27/2800 (pow x 4)))))
35.0ms	(- (* 9/40 (pow x 2)) (log (sqrt (exp (* 27/2800 (pow x 4))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 9/40 (pow x 2))
434.0ms	(log (sqrt (exp (* 27/2800 (pow x 4)))))
436.0ms	(log (sqrt (exp (* 27/2800 (pow x 4)))))
493.0ms	(- (* 9/40 (pow x 2)) (log (sqrt (exp (* 27/2800 (pow x 4))))))

simplify151.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	320	847
1	960	795
2	3766	791
3	5001	791

prune319.0ms

Filtered

140 candidates to 90 candidates (35.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	140	5	145

Merged error: 0.0b

Counts

145 → 5

regimes38.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.0b

bsearch79.0ms

Steps

Iters	Range		Point
9	0.0004381094517774334	96283.49646244562	2.5070089716143773
6	-0.04448272872103196	-0.010589856477353462	-0.030040886285671604

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	46
1	54	46

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.8s	1602×	body	2560	valid
1.5s	2716×	body	1280	valid
485.0ms	1933×	body	640	valid
145.0ms	918×	body	320	valid
56.0ms	489×	body	160	valid
24.0ms	342×	body	80	valid