Details

sample320.0ms

Algorithm

intervals

Results

38.0ms	207×	body	10240	exit
13.0ms	397×	body	80	nan
8.0ms	251×	body	80	valid
1.0ms	13×	body	160	valid

simplify70.0ms

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: 3.0b

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))
2.9b	(- (exp (* 2.0 x)) 1.0)
3.1b	(- (exp x) 1.0)

rewrite50.0ms

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)
8.0ms	(- (exp x) 1.0)

series209.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
35.0ms	(- (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

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

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)))
2.9b	(fma (- 1.0) 1.0 (exp (+ x x)))
2.9b	(- (exp (* 2.0 x)) 1.0)

rewrite45.0ms

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:

10.0ms	(/ (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)

series255.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
115.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
47.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify112.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (82.0ms)

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

prune651.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize16.0ms

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) (/ 1 (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
2.9b	(fma (- 1.0) 1.0 (exp (+ x x)))
2.9b	(- (exp (* 2.0 x)) 1.0)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
96×	`*-un-lft-identity`
82×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
59×	`associate-r`
25×	`add-exp-log`
15×	`add-cbrt-cube`
13×	`distribute-lft-out`
9×	`prod-diff` `associate-/r/`
8×	`div-exp`
7×	`prod-exp`
6×	`pow1` `add-log-exp`
5×	`associate-l` `div-inv` `unswap-sqr`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3-+` `associate-/r*` `flip-+` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--` `cbrt-unprod` `associate-/l*`
2×	`frac-times` `rec-exp` `1-exp` `associate-*l/` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef`

Counts

4 → 169

Calls

4 calls:

7.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
49.0ms	(* (- (exp (* 2.0 x)) 1.0) (/ 1 (/ (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)

series251.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
114.0ms	(* (- (exp (* 2.0 x)) 1.0) (/ 1 (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
46.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify101.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	734	2227
1	3866	1958
2	5001	1882

prune544.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (exp (* 2.0 x)) 1.0) 3)
0.3b	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
2.9b	(fma (- 1.0) 1.0 (exp (+ x x)))
2.9b	(- (exp (* 2.0 x)) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

6.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
6.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series153.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
29.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	331	742
1	1260	635
2	5001	625

prune309.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes32.0ms

Accuracy

99.2% (0.0b remaining)

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

bsearch88.0ms

Steps

Iters	Range		Point
7	1.0628848468647387e-13	9.049190128523824e-12	1.0770376689435775e-13
7	-1.0593127772646427e-09	-5.361660241782146e-11	-1.1641163077155313e-10

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	37
1	48	37

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6560×	body	10240	exit
380.0ms	12522×	body	80	nan
242.0ms	7448×	body	80	valid
54.0ms	675×	body	160	valid