Details

sample353.0ms

Algorithm

intervals

Results

47.0ms	242×	body	10240	exit
11.0ms	374×	body	80	nan
9.0ms	239×	body	80	valid
2.0ms	24×	body	160	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.1b	(- (exp (* 2.0 x)) 1.0)
5.2b	(- (exp x) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`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/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

13.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
14.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series200.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
54.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
34.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify122.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4287	1301
3	5003	1293

prune309.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.2b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.2b	(- (exp x) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
11×	`sqrt-prod` `add-log-exp`
5×	`pow1` `add-cube-cbrt` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sqrt-pow1` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `exp-prod` `exp-to-pow` `flip3-+` `pow1/2` `sum-log` `flip-+`

Counts

4 → 60

Calls

4 calls:

1.0ms	(sqrt (exp (* 2.0 x)))
6.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series127.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (exp (* 2.0 x)))
41.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
48.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify118.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	209	434
1	530	405
2	1324	402
3	3833	401
4	5001	401

prune192.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* 2.0 x)) 1.0)
0.1b	(pow (sqrt (exp (* 2.0 x))) 3)
5.2b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.2b	(- (exp x) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
12×	`sqrt-prod`
11×	`add-log-exp`
9×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `cube-prod`
5×	`add-exp-log` `pow-pow` `add-cbrt-cube` `difference-of-squares`
3×	`pow-unpow` `sqrt-pow1` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`+-commutative` `cube-mult` `pow-to-exp` `exp-prod` `exp-to-pow` `flip3-+` `pow1/2` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `flip-+` `distribute-lft-out` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

3.0ms	(+ (exp (* 2.0 x)) 1.0)
3.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series124.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (exp (* 2.0 x)) 1.0)
44.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	321	517
1	1205	474
2	5001	464

prune272.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`add-log-exp` `unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r`
4×	`associate-*r/` `prod-exp`
3×	`cbrt-undiv` `sum-log` `div-inv`
2×	`distribute-rgt-in` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `flip3-+` `frac-add` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`
1×	`+-commutative` `associate-+r+` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--`

Counts

4 → 221

Calls

4 calls:

15.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
43.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
5.0ms	(/ (pow x 2) (sqrt 2.0))
3.0ms	(/ x (sqrt 2.0))

series275.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
69.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
62.0ms	(/ (pow x 2) (sqrt 2.0))
53.0ms	(/ x (sqrt 2.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	723	1889
1	3042	1708
2	5001	1694

prune482.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

77.6% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.4b

bsearch37.0ms

Steps

Iters	Range		Point
6	-2.992705010292926e-10	-3.730896500397528e-11	-4.755248129243865e-11

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	27
1	38	27

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6536×	body	10240	exit
369.0ms	12106×	body	80	nan
244.0ms	7401×	body	80	valid
63.0ms	730×	body	160	valid