Details

analyze1.4s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample214.0ms

Algorithm

intervals

Results

118.0ms	47×	body	2560	valid
55.0ms	85×	body	1280	valid
21.0ms	61×	body	640	valid
5.0ms	25×	body	320	valid
3.0ms	19×	body	160	valid
2.0ms	19×	body	80	valid

simplify461.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

prune21.0ms

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: 31.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.6b	(- x (tan x))
2.6b	(- x (sin x))

rewrite20.0ms

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 → 78

Calls

3 calls:

7.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series37.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
13.0ms	(- x (sin x))

simplify62.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune101.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.1b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
2.6b	(- x (tan x))
2.6b	(- x (sin x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
32×	`log-pow`
31×	`exp-prod`
28×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 122

Calls

4 calls:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series43.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
13.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
10.0ms	(- x (tan x))
8.0ms	(- x (sin x))

simplify40.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4969	1705
1	4969	1705

prune133.0ms

Filtered

96 candidates to 134 candidates (-39.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	133	5	138

Merged error: 0.0b

Counts

138 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
0.1b	(* x (* x 9/40))
0.2b	(* x 9/40)
17.1b	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 74

Calls

4 calls:

5.0ms	(* (pow x 4) -27/2800)
6.0ms	(* x (* x 9/40))
3.0ms	(* x 9/40)
8.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

series14.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (pow x 4) -27/2800)
3.0ms	(* x (* x 9/40))
2.0ms	(* x 9/40)
6.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

simplify56.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4903	646
1	4903	646

prune108.0ms

Filtered

52 candidates to 86 candidates (-65.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	86	5	91

Merged error: 0.0b

Counts

91 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
0.1b	(* x (* x 9/40))
0.2b	(* x 9/40)
17.1b	(+ (+ (* x (* x 9/40)) -1/2) (* (pow x 4) -27/2800))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 74

Calls

4 calls:

5.0ms	(* (pow x 4) -27/2800)
4.0ms	(* x (* x 9/40))
3.0ms	(* x 9/40)
8.0ms	(+ (+ (* x (* x 9/40)) -1/2) (* (pow x 4) -27/2800))

series13.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (pow x 4) -27/2800)
3.0ms	(* x (* x 9/40))
2.0ms	(* x 9/40)
5.0ms	(+ (+ (* x (* x 9/40)) -1/2) (* (pow x 4) -27/2800))

simplify51.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4921	646
1	4921	646

prune89.0ms

Filtered

52 candidates to 86 candidates (-65.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	86	5	91

Merged error: 0.0b

Counts

91 → 5

regimes95.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch34.0ms

Steps

Iters	Range		Point
7	0.015364448262276292	1.0310884387662207	0.025838072108942886
9	-2853.066991623172	-0.0024591482066684753	-0.024104041126318445

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	33
1	50	33

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.0s	1602×	body	2560	valid
1.7s	2721×	body	1280	valid
521.0ms	1971×	body	640	valid
172.0ms	890×	body	320	valid
64.0ms	470×	body	160	valid
27.0ms	346×	body	80	valid

Details

analyze1.4s

sample214.0ms

simplify461.0ms

prune21.0ms

localize10.0ms

rewrite20.0ms

series37.0ms

simplify62.0ms

prune101.0ms

localize11.0ms

rewrite30.0ms

series43.0ms

simplify40.0ms

prune133.0ms

localize9.0ms

rewrite24.0ms

series14.0ms

simplify56.0ms

prune108.0ms

localize9.0ms

rewrite22.0ms

series13.0ms

simplify51.0ms

prune89.0ms

regimes95.0ms

bsearch34.0ms

simplify2.0ms

end0.0ms

sample6.6s

Profiling