Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	248×	body	80	nan
5.0ms	57×	body	640	valid
4.0ms	149×	body	80	valid
4.0ms	29×	body	1280	valid
1.0ms	18×	body	320	valid
0.0ms	3×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6

prune2.0ms

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: 17.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
1.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
69×	`times-frac`
46×	`sqrt-prod`
40×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `clear-num` `associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `frac-sub` `flip--` `flip-+`

Counts

3 → 117

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
35.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series258.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ 1.0 (sqrt (+ x 1.0)))
45.0ms	(/ 1.0 (sqrt x))
133.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	410	1006
1	1310	954
2	5001	912

prune267.0ms

Filtered

126 candidates to 84 candidates (66.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	115	11	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	11	127

Merged error: 17.4b

Counts

127 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt x))
0.2b	(/ 1.0 (sqrt x))
0.3b	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
7.7b	(- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
155×	`sqrt-prod`
112×	`times-frac`
56×	`difference-of-squares`
42×	`*-un-lft-identity`
36×	`add-cube-cbrt`
33×	`associate-r`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`frac-times` `sqrt-div`
8×	`div-inv`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`flip3--` `associate-l` `frac-sub` `flip--`
4×	`flip3-+` `frac-add` `flip-+` `distribute-lft-out--`
3×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `distribute-lft-out`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 190

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt x))
4.0ms	(/ 1.0 (sqrt x))
142.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
72.0ms	(- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1.0 (sqrt x))
43.0ms	(/ 1.0 (sqrt x))
601.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
498.0ms	(- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

simplify121.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	933	3488
1	4248	3292
2	5001	3280

prune531.0ms

Filtered

202 candidates to 125 candidates (61.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	195	7	202
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	200	13	213

Merged error: 11.5b

Counts

213 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt x))
0.2b	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
0.3b	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (/ (* (sqrt 1.0) (- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))))
1.2b	(- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

79×	`sqrt-prod`
65×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
27×	`add-cube-cbrt`
26×	`add-exp-log` `add-cbrt-cube`
19×	`times-frac`
17×	`associate-r`
14×	`associate-l`
12×	`pow1`
10×	`sqrt-div` `prod-exp` `cbrt-unprod` `unswap-sqr`
9×	`difference-of-squares`
8×	`sqrt-pow1`
6×	`pow-prod-down` `associate-/r*` `add-log-exp`
5×	`cbrt-undiv` `associate-*r/` `div-exp`
4×	`flip3-+` `pow1/2` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--`
3×	`frac-times` `associate-l/` `associate-/l`
2×	`frac-add` `associate-/r/` `*-commutative`
1×	`sub-neg` `flip3--` `frac-2neg` `sqrt-unprod` `diff-log` `clear-num` `flip--`

Counts

4 → 149

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt x))
11.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
92.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (/ (* (sqrt 1.0) (- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))))
12.0ms	(- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1.0 (sqrt x))
121.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
935.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (/ (* (sqrt 1.0) (- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))))
172.0ms	(- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1500	3014
1	5002	2652

prune589.0ms

Filtered

161 candidates to 115 candidates (71.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	160	14	174

Merged error: 11.5b

Counts

174 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
0.3b	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (/ (* (sqrt 1.0) (log (exp (- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))))
1.1b	(log (exp (- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))))
1.2b	(- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

95×	`sqrt-prod`
70×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
24×	`add-exp-log` `add-cbrt-cube`
18×	`difference-of-squares`
17×	`associate-r` `log-pow`
16×	`exp-prod`
14×	`add-cube-cbrt` `associate-l`
13×	`pow1`
10×	`sqrt-div` `prod-exp` `cbrt-unprod` `unswap-sqr`
8×	`sqrt-pow1` `distribute-lft-out--`
6×	`pow-prod-down` `add-log-exp`
5×	`log-prod` `associate-*r/` `distribute-lft-out`
4×	`cbrt-undiv` `flip3-+` `pow1/2` `div-exp` `flip-+`
3×	`frac-times` `associate-*l/` `div-inv`
2×	`sub-neg` `exp-sum` `frac-add` `associate-/r/` `*-commutative`
1×	`log-div` `flip3--` `times-frac` `exp-diff` `sqrt-unprod` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 141

Calls

4 calls:

13.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
92.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (/ (* (sqrt 1.0) (log (exp (- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))))
12.0ms	(log (exp (- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))))
11.0ms	(- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))

series1.4s

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
921.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (/ (* (sqrt 1.0) (log (exp (- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))))
178.0ms	(log (exp (- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))))
174.0ms	(- (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1398	3153
1	5002	2750

prune559.0ms

Filtered

153 candidates to 103 candidates (67.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	152	15	167

Merged error: 11.5b

Counts

167 → 15

regimes83.0ms

Accuracy

98.1% (0.2b remaining)

Error of 10.5b against oracle of 10.3b and baseline of 19.7b

bsearch52.0ms

Steps

Iters	Range		Point
9	164.2181510969774	3048118974.682059	7077.048346062627

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	27
1	45	27

end0.0ms

sample831.0ms

Algorithm

intervals

Results

177.0ms	1839×	body	640	valid
174.0ms	7900×	body	80	nan
133.0ms	1106×	body	1280	valid
106.0ms	4112×	body	80	valid
46.0ms	630×	body	320	valid
15.0ms	313×	body	160	valid