Details

sample333.0ms

Algorithm

intervals

Results

37.0ms	192×	body	10240	exit
13.0ms	393×	body	80	nan
8.0ms	245×	body	80	valid
1.0ms	13×	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	41	7
3	75	7
4	182	7
5	576	7
6	2666	7
7	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize21.0ms

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))
3.5b	(- (exp (* 2.0 x)) 1.0)
3.5b	(- (exp x) 1.0)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
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 → 155

Calls

4 calls:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
16.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
9.0ms	(- (exp x) 1.0)

series203.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
34.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify60.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	480	1694
1	1523	1484
2	5001	1470

prune392.0ms

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	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
3.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.5b	(- (exp (* 2.0 x)) 1.0)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
171×	`*-un-lft-identity`
127×	`add-sqr-sqrt`
87×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
8×	`div-inv` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-neg`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `fma-udef`

Counts

4 → 206

Calls

4 calls:

7.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
21.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series254.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
120.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
42.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms	(- (exp (* 2.0 x)) 1.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	805	3596
1	3551	3384
2	5003	3382

prune663.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
3.5b	(- (exp (* 2.0 x)) 1.0)
3.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.5b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`prod-diff`
8×	`add-log-exp`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `expm1-log1p-u` `pow-pow` `fma-neg` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `cube-prod`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`cube-mult` `pow-to-exp` `distribute-rgt-out--` `unpow3` `pow-exp` `fma-udef` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

2.0ms	(pow (exp x) 3)
5.0ms	(- (exp (* 2.0 x)) 1.0)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
3.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series124.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (exp x) 3)
25.0ms	(- (exp (* 2.0 x)) 1.0)
44.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
31.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	374	523
1	1648	414
2	5002	407

prune383.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

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)))))
0.4b	(/ x (sqrt 2.0))
0.4b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.4b	(/ (pow x 2) (sqrt 2.0))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac`
176×	`add-sqr-sqrt`
151×	`*-un-lft-identity`
149×	`add-cube-cbrt`
78×	`prod-diff`
67×	`sqrt-prod`
52×	`associate-l`
41×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`div-inv` `add-log-exp` `unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r`
4×	`expm1-log1p-u` `associate-*r/` `prod-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `sum-log`
2×	`frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `frac-add` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`
1×	`+-commutative` `associate-+r+` `fma-def` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--`

Counts

4 → 308

Calls

4 calls:

13.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
3.0ms	(/ x (sqrt 2.0))
56.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
5.0ms	(/ (pow x 2) (sqrt 2.0))

series281.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
57.0ms	(/ x (sqrt 2.0))
65.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
65.0ms	(/ (pow x 2) (sqrt 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1334	4363
1	5002	3450

prune568.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes25.0ms

Accuracy

76.4% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.8b

bsearch23.0ms

Steps

Iters	Range		Point
3	-9.091202463712598e-16	-7.520341406059738e-16	-8.528320854014055e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	35
1	50	35

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	6629×	body	10240	exit
369.0ms	12553×	body	80	nan
238.0ms	7427×	body	80	valid
57.0ms	715×	body	160	valid