Details

sample400.0ms

Algorithm

intervals

Results

37.0ms	206×	body	10240	exit
33.0ms	375×	body	80	nan
9.0ms	241×	body	80	valid
1.0ms	19×	body	160	valid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 4.1b

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))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp x) 1.0)

rewrite107.0ms

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:

28.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
37.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
20.0ms	(- (exp (* 2.0 x)) 1.0)
15.0ms	(- (exp x) 1.0)

series201.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

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

prune379.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
4.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.5b	(- (exp (* 2.0 x)) 1.0)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`prod-diff`
8×	`add-log-exp`
7×	`pow1`
5×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `fma-neg` `flip-+`
2×	`frac-times` `sqrt-pow1` `associate-*r/`
1×	`+-commutative` `sub-neg` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-*l/` `sum-log` `sqrt-prod` `flip--` `fma-udef` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 73

Calls

4 calls:

18.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
9.0ms	(+ (exp x) 1.0)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
16.0ms	(- (exp (* 2.0 x)) 1.0)

series230.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
8.0ms	(+ (exp x) 1.0)
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	361	673
1	1258	564
2	5002	559

prune269.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (fma (sqrt (exp x)) (sqrt (exp x)) 1.0)))
0.0b	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
4.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.5b	(- (exp (* 2.0 x)) 1.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`sqrt-pow1` `fma-udef`
1×	`sub-neg` `flip3--` `pow1/2` `sqrt-div` `diff-log` `pow-prod-down` `associate-*l/` `sqrt-prod` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 62

Calls

4 calls:

12.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (fma (sqrt (exp x)) (sqrt (exp x)) 1.0)))
0.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
14.0ms	(- (exp (* 2.0 x)) 1.0)

series297.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (fma (sqrt (exp x)) (sqrt (exp x)) 1.0)))
40.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
28.0ms	(- (exp (* 2.0 x)) 1.0)

simplify114.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	274	645
1	849	518
2	4103	502
3	5001	486

prune252.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (exp (* 2.0 x)) 1.0) 3)
0.1b	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
4.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.5b	(- (exp (* 2.0 x)) 1.0)

rewrite49.0ms

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:

16.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
14.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
14.0ms	(- (exp (* 2.0 x)) 1.0)

series148.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
30.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (35.0ms)

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

prune312.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes24.0ms

Accuracy

71.5% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 2.8b

bsearch45.0ms

Steps

Iters	Range		Point
8	-5.931762247777049e-05	-2.2707086624102254e-09	-1.2754467331002943e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	19
1	27	19

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6750×	body	10240	exit
368.0ms	12617×	body	80	nan
236.0ms	7426×	body	80	valid
54.0ms	702×	body	160	valid