Details

sample324.0ms

Algorithm

intervals

Results

37.0ms	198×	body	10240	exit
13.0ms	434×	body	80	nan
8.0ms	236×	body	80	valid
3.0ms	24×	body	160	valid

simplify72.0ms

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: 4.3b

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))
5.1b	(- (exp (* 2.0 x)) 1.0)
5.1b	(- (exp x) 1.0)

rewrite38.0ms

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:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series204.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
56.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
33.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

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

prune402.0ms

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)
5.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.1b	(- (exp (* 2.0 x)) 1.0)

rewrite22.0ms

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:

9.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
5.0ms	(+ (exp x) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series235.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(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)

simplify43.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (35.0ms)

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

prune290.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
5.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.1b	(- (exp (* 2.0 x)) 1.0)

rewrite23.0ms

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:

7.0ms	(sqrt (* (/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
8.0ms	(+ (exp x) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series372.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(sqrt (* (/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
13.0ms	(+ (exp x) 1.0)
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	371	707
1	1301	596
2	5002	591

prune338.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
5.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.1b	(- (exp (* 2.0 x)) 1.0)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod` `fma-neg` `sqrt-prod`
2×	`fma-udef`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

2.0ms	(sqrt (exp x))
1.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series120.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp x))
38.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1.0)
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify104.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	242	461
1	681	350
2	3184	337
3	5001	309

prune315.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

72.1% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 2.7b

bsearch47.0ms

Steps

Iters	Range		Point
7	-5.6669034693225635e-12	-5.8829093822384e-14	-5.3888208797845926e-12

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6661×	body	10240	exit
365.0ms	12605×	body	80	nan
238.0ms	7407×	body	80	valid
52.0ms	699×	body	160	valid