Details

sample319.0ms

Algorithm

intervals

Results

34.0ms	173×	body	10240	exit
13.0ms	381×	body	80	nan
8.0ms	237×	body	80	valid
2.0ms	23×	body	160	valid

simplify74.0ms

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: 5.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.3b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.1b	(- (exp (* 2.0 x)) 1.0)
5.2b	(- (exp x) 1.0)

rewrite49.0ms

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:

16.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
13.0ms	(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)

series200.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
32.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

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

prune379.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.3b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
5.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.1b	(- (exp (* 2.0 x)) 1.0)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

315×	`times-frac`
279×	`*-un-lft-identity`
219×	`add-sqr-sqrt`
137×	`add-cube-cbrt`
95×	`sqrt-prod`
38×	`distribute-lft-out--` `difference-of-squares`
33×	`distribute-lft-out`
24×	`associate-/r/`
18×	`associate-/r*`
13×	`div-inv`
11×	`flip3-+` `flip-+`
9×	`add-exp-log` `prod-diff` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `rem-sqrt-square` `fma-neg` `div-exp`
2×	`flip3--` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-sub` `clear-num` `fma-udef`

Counts

4 → 281

Calls

4 calls:

23.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
22.0ms	(sqrt (/ (- (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)

series328.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
149.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms	(- (exp (* 2.0 x)) 1.0)

simplify138.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	945	5898
1	3770	5653
2	5001	5535

prune852.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 391

Calls

4 calls:

16.0ms	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
53.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
5.0ms	(/ (pow x 2) (sqrt 2.0))
3.0ms	(/ x (sqrt 2.0))

series317.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
67.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
62.0ms	(/ (pow x 2) (sqrt 2.0))
53.0ms	(/ x (sqrt 2.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

403 → 403

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1365	5373
1	5002	4187

prune826.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))
2.6b	(exp (log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
26.1b	(log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`sqrt-prod`
21×	`unpow-prod-down`
12×	`add-exp-log` `associate-/r*`
11×	`associate-/l*`
8×	`add-cbrt-cube`
7×	`unpow2` `sqr-pow`
6×	`pow1` `log-prod`
4×	`expm1-log1p-u` `log-div` `exp-prod` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `exp-diff` `clear-num` `log-pow` `flip-+` `div-inv`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `rem-exp-log`

Counts

4 → 154

Calls

4 calls:

5.0ms	(/ (pow x 2) (sqrt 2.0))
3.0ms	(/ x (sqrt 2.0))
4.0ms	(exp (log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
3.0ms	(log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (pow x 2) (sqrt 2.0))
51.0ms	(/ x (sqrt 2.0))
137.0ms	(exp (log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))))
215.0ms	(log (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	457	1344
1	1684	1182
2	5001	1149

prune411.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes20.0ms

Accuracy

72.5% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch40.0ms

Steps

Iters	Range		Point
5	-7.455527952367615e-16	-3.171438052781698e-16	-7.195205579931451e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	28
1	42	28

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6785×	body	10240	exit
393.0ms	12465×	body	80	nan
246.0ms	7407×	body	80	valid
60.0ms	729×	body	160	valid