Details

sample327.0ms

Algorithm

intervals

Results

45.0ms	226×	body	10240	exit
14.0ms	414×	body	80	nan
8.0ms	246×	body	80	valid
2.0ms	21×	body	160	valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

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: 5.2b

localize12.0ms

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)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series203.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
31.0ms	(- (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

prune388.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`sqrt-div` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-/r*`
2×	`frac-times` `flip3--` `sqrt-pow1` `flip3-+` `associate-*r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `associate-*l/` `clear-num` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 96

Calls

4 calls:

7.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
9.0ms	(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)

series405.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
151.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
27.0ms	(- (exp (* 2.0 x)) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	439	1178
1	1619	1042
2	5001	1028

prune347.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`sqrt-div` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-/r*`
2×	`frac-times` `flip3--` `sqrt-pow1` `flip3-+` `associate-*r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `associate-*l/` `clear-num` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 96

Calls

4 calls:

7.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
10.0ms	(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)

series411.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
152.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
38.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
27.0ms	(- (exp (* 2.0 x)) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	439	1178
1	1619	1042
2	5001	1028

prune399.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (fma (- 1.0) 1.0 (exp (+ x x))))
0.5b	(sqrt (* (/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (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)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt` `*-un-lft-identity`
64×	`cbrt-prod`
57×	`times-frac`
47×	`add-cube-cbrt`
20×	`unpow-prod-down` `cube-prod`
19×	`associate-/l*`
9×	`prod-diff` `distribute-lft-out--` `difference-of-squares`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
5×	`sqrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `sqr-pow`
3×	`fma-neg` `associate-/r*`
2×	`cube-div` `frac-times` `cbrt-div` `flip3--` `sqrt-pow1` `flip3-+` `associate-*r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `associate-*l/` `clear-num` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 151

Calls

4 calls:

10.0ms	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (fma (- 1.0) 1.0 (exp (+ x x))))
13.0ms	(sqrt (* (/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (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)

series409.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (fma (- 1.0) 1.0 (exp (+ x x))))
152.0ms	(sqrt (* (/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
38.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
28.0ms	(- (exp (* 2.0 x)) 1.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	534	2296
1	2171	2105
2	5002	2088

prune483.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.5b

regimes29.0ms

Accuracy

72.4% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 2.9b

bsearch54.0ms

Steps

Iters	Range		Point
9	-2.8228108650395133e-08	-2.5686370651019963e-14	-2.5012786943274603e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6729×	body	10240	exit
410.0ms	12551×	body	80	nan
253.0ms	7458×	body	80	valid
54.0ms	686×	body	160	valid