Details

sample341.0ms

Algorithm

intervals

Results

55.0ms	226×	body	10240	exit
13.0ms	414×	body	80	nan
8.0ms	246×	body	80	valid
2.0ms	21×	body	160	valid

simplify74.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.5b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.8b	(- (exp (* 2.0 x)) 1.0)
4.9b	(- (exp x) 1.0)

rewrite37.0ms

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:

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

series205.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
92.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
35.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

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

prune403.0ms

Filtered

167 candidates to 110 candidates (65.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.5b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
4.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.8b	(- (exp (* 2.0 x)) 1.0)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
155×	`*-un-lft-identity`
123×	`add-sqr-sqrt`
95×	`sqrt-prod`
79×	`add-cube-cbrt`
19×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
13×	`associate-/r/`
9×	`prod-diff`
7×	`div-inv`
6×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`rem-sqrt-square` `fma-neg` `associate-/l*`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-exp` `clear-num` `flip--` `fma-udef`

Counts

4 → 183

Calls

4 calls:

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

series287.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
155.0ms	(sqrt (/ (- (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)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify93.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	836	3484
1	2947	3301
2	5001	3182

prune613.0ms

Filtered

195 candidates to 133 candidates (68.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3)))
4.8b	(- (exp (* 2.0 x)) 1.0)
4.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.9b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `times-frac`
25×	`add-cube-cbrt`
20×	`distribute-lft-out`
16×	`unpow-prod-down` `cube-prod`
10×	`prod-diff`
9×	`associate-/r*`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `fma-neg` `sum-cubes` `log1p-expm1-u`
3×	`associate-/l*`
2×	`sub-neg` `flip3--` `diff-log` `associate-/r/` `flip--`
1×	`cbrt-undiv` `distribute-rgt-out--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

15.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3)))
5.0ms	(- (exp (* 2.0 x)) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
4.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series193.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3)))
24.0ms	(- (exp (* 2.0 x)) 1.0)
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
31.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	448	1251
1	1811	1097
2	5001	1086

prune465.0ms

Filtered

122 candidates to 80 candidates (65.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3)))
4.8b	(- (exp (* 2.0 x)) 1.0)
4.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.9b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `times-frac`
25×	`add-cube-cbrt`
20×	`distribute-lft-out`
16×	`unpow-prod-down` `cube-prod`
10×	`prod-diff`
9×	`associate-/r*`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `fma-neg` `sum-cubes` `log1p-expm1-u`
3×	`associate-/l*`
2×	`sub-neg` `flip3--` `diff-log` `associate-/r/` `flip--`
1×	`cbrt-undiv` `distribute-rgt-out--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

13.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3)))
5.0ms	(- (exp (* 2.0 x)) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
4.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series192.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3)))
25.0ms	(- (exp (* 2.0 x)) 1.0)
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
31.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	448	1251
1	1811	1097
2	5001	1086

prune515.0ms

Filtered

122 candidates to 80 candidates (65.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.5b

regimes33.0ms

Accuracy

73.1% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 2.9b

bsearch68.0ms

Steps

Iters	Range		Point
9	-2.8228108650395133e-08	-2.5686370651019963e-14	-2.6649226804399346e-11

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	37
1	46	37

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6729×	body	10240	exit
378.0ms	12551×	body	80	nan
240.0ms	7458×	body	80	valid
53.0ms	686×	body	160	valid