Details

sample320.0ms

Algorithm

intervals

Results

36.0ms	187×	body	10240	exit
12.0ms	414×	body	80	nan
9.0ms	244×	body	80	valid
2.0ms	19×	body	160	valid

simplify84.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.6b	(- (exp (* 2.0 x)) 1.0)
3.7b	(- (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)))
15.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series197.0ms

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))
32.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify125.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (108.0ms)

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

prune313.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

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))
3.7b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.7b	(- (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)))
7.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series126.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (exp (* 2.0 x)))
40.0ms	(+ (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

prune213.0ms

Filtered

72 candidates to 49 candidates (68.1%)

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	(/ (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))))
0.0b	(pow (sqrt (exp (* 2.0 x))) 3)
3.7b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.7b	(- (exp x) 1.0)

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
44×	`sqrt-prod`
39×	`times-frac`
38×	`unpow-prod-down` `cube-prod`
37×	`add-sqr-sqrt`
36×	`distribute-lft-out`
27×	`add-cube-cbrt`
13×	`associate-/l*`
9×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`pow-pow` `difference-of-squares`
4×	`sum-cubes`
3×	`pow-unpow` `flip3--` `sqrt-pow1` `associate-/r*` `flip--` `distribute-lft-out--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `exp-prod` `exp-to-pow` `frac-2neg` `flip3-+` `pow1/2` `unpow3` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `flip-+` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 137

Calls

4 calls:

101.0ms	(/ (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 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)

series545.0ms

Counts

4 → 12

Calls

4 calls:

438.0ms	(/ (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))))
44.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
48.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify100.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	677	2524
1	3327	2375
2	5002	2365

prune438.0ms

Filtered

149 candidates to 76 candidates (51.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
0.0b	(* x (+ 1.0 (* 0.5 x)))
25.4b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-r` `associate-l` `sqrt-prod` `flip-+`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `sqrt-div` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

4.0ms	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
7.0ms	(* x (+ 1.0 (* 0.5 x)))
6.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series163.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
64.0ms	(* x (+ 1.0 (* 0.5 x)))
78.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	308	385
1	1305	364
2	5001	353

prune103.0ms

Filtered

59 candidates to 44 candidates (74.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

77.2% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.3b

bsearch31.0ms

Steps

Iters	Range		Point
6	-1.534026600097144e-05	-1.1282193140217931e-06	-1.2337766313196286e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	22
1	35	22

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6618×	body	10240	exit
382.0ms	12905×	body	80	nan
246.0ms	7426×	body	80	valid
54.0ms	709×	body	160	valid