Details

sample324.0ms

Algorithm

intervals

Results

38.0ms	197×	body	10240	exit
13.0ms	399×	body	80	nan
7.0ms	227×	body	80	valid
3.0ms	34×	body	160	valid

simplify86.0ms

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	2657	7
7	5001	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.9b

Counts

2 → 1

localize11.0ms

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))
6.7b	(- (exp (* 2.0 x)) 1.0)
6.8b	(- (exp x) 1.0)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
51×	`times-frac`
43×	`add-cube-cbrt`
31×	`sqrt-prod`
26×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
15×	`sqrt-div`
10×	`associate-/r` `associate-/l`
8×	`add-log-exp`
6×	`add-exp-log` `flip3--` `fma-neg` `add-cbrt-cube` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
2×	`sub-neg` `rem-sqrt-square` `frac-2neg` `diff-log` `clear-num` `div-inv`
1×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `div-sub` `div-exp`

Counts

4 → 169

Calls

4 calls:

15.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
14.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
7.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series214.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
36.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	495	1844
1	1504	1646
2	5002	1629

prune352.0ms

Filtered

181 candidates to 120 candidates (66.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	3	182

Merged error: 0.0b

Counts

182 → 3

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)
6.7b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.7b	(- (exp (* 2.0 x)) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
41×	`sqrt-div`
30×	`sqrt-prod`
29×	`add-cube-cbrt`
26×	`frac-times`
19×	`associate-l`
17×	`times-frac`
15×	`flip3-+` `flip-+` `associate-/l*`
13×	`associate-*l/`
9×	`prod-diff` `associate-/r*`
8×	`add-log-exp`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/l/`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `associate-r` `add-cbrt-cube` `flip--` `log1p-expm1-u` `unswap-sqr`
3×	`rem-sqrt-square` `fma-def` `frac-2neg` `fma-neg` `clear-num`
2×	`sqrt-pow1` `associate-*r/` `distribute-lft-out`
1×	`+-commutative` `sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sum-log` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 141

Calls

4 calls:

25.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
4.0ms	(+ (exp x) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
8.0ms	(- (exp (* 2.0 x)) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(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)
47.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify118.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	979	2155
1	4638	2017
2	5001	2014

prune446.0ms

Filtered

153 candidates to 116 candidates (75.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	152	4	156

Merged error: 0b

Counts

156 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))
0.1b	(pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)
6.7b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.7b	(- (exp (* 2.0 x)) 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`cbrt-prod`
6×	`unpow-prod-down` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u`
3×	`fma-neg`
2×	`unpow3` `rem-cbrt-cube` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow1/3` `diff-log` `pow-exp` `flip--` `fma-udef` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 79

Calls

4 calls:

2.0ms	(cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))
2.0ms	(pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
8.0ms	(- (exp (* 2.0 x)) 1.0)

series188.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))
72.0ms	(pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)
42.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	285	621
1	988	517
2	5001	511

prune244.0ms

Filtered

91 candidates to 59 candidates (64.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	91	4	95

Merged error: 0b

Counts

95 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
6.7b	(- (exp (* 2.0 x)) 1.0)
6.7b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.8b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

209×	`add-sqr-sqrt`
189×	`prod-diff`
139×	`*-un-lft-identity`
126×	`add-cube-cbrt`
93×	`associate-r`
88×	`associate-l`
41×	`swap-sqr`
35×	`*-commutative` `unswap-sqr`
18×	`fma-neg`
11×	`difference-of-squares`
8×	`distribute-rgt-out--` `add-log-exp`
7×	`distribute-lft-out--`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `exp-prod`
2×	`sub-neg` `flip3--` `diff-log` `pow-exp` `flip--`
1×	`pow-to-exp` `unpow3` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 296

Calls

4 calls:

3.0ms	(pow (exp x) 3)
8.0ms	(- (exp (* 2.0 x)) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
22.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series135.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (exp x) 3)
29.0ms	(- (exp (* 2.0 x)) 1.0)
42.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
39.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify111.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	810	4326
1	2600	1919
2	5002	1913

prune452.0ms

Filtered

308 candidates to 84 candidates (27.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	308	0	308
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	308	4	312

Merged error: 0b

Counts

312 → 4

regimes32.0ms

Accuracy

73.9% (0.8b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.0b

bsearch40.0ms

Steps

Iters	Range		Point
7	-1.2080237657941953e-11	-3.4401241170895896e-13	-1.1933942233902218e-11

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	16
1	27	16

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6649×	body	10240	exit
390.0ms	12603×	body	80	nan
248.0ms	7352×	body	80	valid
60.0ms	763×	body	160	valid