Details

sample148.0ms

Algorithm

intervals

Results

48.0ms	281×	body	80	nan
43.0ms	256×	body	80	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	50	17
1	108	17
2	389	17
3	1761	17
4	5002	17

prune5.0ms

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: 3.0b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))
0.3b	(/ 2.0 (* t 3.0))
2.0b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
4.4b	(/ (* z (sqrt (+ t a))) t)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

77×	`prod-diff`
76×	`*-un-lft-identity`
62×	`associate--r+`
50×	`add-sqr-sqrt`
48×	`add-cube-cbrt`
42×	`times-frac`
40×	`distribute-rgt-in` `distribute-lft-in`
21×	`associate-r`
20×	`frac-sub`
18×	`exp-sum`
16×	`add-cbrt-cube`
15×	`add-exp-log`
14×	`div-inv` `distribute-lft-out`
9×	`flip3--` `flip--`
8×	`frac-times`
7×	`fma-neg`
6×	`pow1` `associate-*r/` `add-log-exp`
5×	`sub-neg`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3-+` `div-exp` `associate-/r` `flip-+` `log1p-expm1-u` `associate-/l`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `sqrt-div` `associate-*l/` `associate--l+` `clear-num` `associate-/l/`
1×	`diff-log` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 190

Calls

4 calls:

16.0ms	(* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))
5.0ms	(/ 2.0 (* t 3.0))
26.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
8.0ms	(/ (* z (sqrt (+ t a))) t)

series542.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))
15.0ms	(/ 2.0 (* t 3.0))
201.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
81.0ms	(/ (* z (sqrt (+ t a))) t)

simplify63.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1461	3222
1	5001	2846

prune882.0ms

Filtered

202 candidates to 147 candidates (72.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	198	5	203

Merged error: 0.5b

Counts

203 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
1.7b	(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series883.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt t)
176.0ms	(cbrt t)
181.0ms	(cbrt t)
343.0ms	(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	144	371
1	345	322
2	1221	312
3	5001	306

prune358.0ms

Filtered

61 candidates to 54 candidates (88.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	61	5	66

Merged error: 0.5b

Counts

66 → 5

localize38.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
4.4b	(/ (* z (sqrt (+ t a))) t)
4.4b	(/ (* z (sqrt (+ t a))) t)
4.4b	(/ (* z (sqrt (+ t a))) t)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
63×	`prod-diff`
62×	`associate--r+`
44×	`add-sqr-sqrt` `add-cube-cbrt`
39×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
20×	`frac-sub`
19×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-out`
13×	`div-inv`
10×	`associate-*r/`
9×	`flip3--` `associate-/r*` `flip--`
8×	`frac-times`
7×	`fma-neg`
6×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `flip-+` `associate-/l/` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`
2×	`associate-*l/` `associate--l+`
1×	`diff-log`

Counts

4 → 179

Calls

4 calls:

25.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
8.0ms	(/ (* z (sqrt (+ t a))) t)
8.0ms	(/ (* z (sqrt (+ t a))) t)
8.0ms	(/ (* z (sqrt (+ t a))) t)

series432.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
82.0ms	(/ (* z (sqrt (+ t a))) t)
82.0ms	(/ (* z (sqrt (+ t a))) t)
82.0ms	(/ (* z (sqrt (+ t a))) t)

simplify56.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1203	2741
1	5001	2421

prune1.4s

Filtered

191 candidates to 141 candidates (73.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	191	5	196

Merged error: 0.5b

Counts

196 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* t 3.0))
0.7b	(log1p (expm1 (/ 2.0 (* t 3.0))))
3.0b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log1p (expm1 (/ 2.0 (* t 3.0)))))))
4.4b	(/ (* z (sqrt (+ t a))) t)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
31×	`prod-diff`
30×	`associate--r+`
26×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`distribute-rgt-in` `distribute-lft-in`
14×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`frac-sub`
7×	`flip3--` `fma-neg` `flip--`
6×	`distribute-lft-out` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-times` `associate-r/` `div-exp` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l*`
3×	`sub-neg`
2×	`frac-2neg` `sqrt-div` `associate-*l/` `prod-exp` `associate--l+` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`log1p-udef` `flip3-+` `diff-log` `log1p-expm1` `flip-+`

Counts

4 → 125

Calls

4 calls:

5.0ms	(/ 2.0 (* t 3.0))
1.0ms	(log1p (expm1 (/ 2.0 (* t 3.0))))
20.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log1p (expm1 (/ 2.0 (* t 3.0)))))))
8.0ms	(/ (* z (sqrt (+ t a))) t)

series875.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 2.0 (* t 3.0))
513.0ms	(log1p (expm1 (/ 2.0 (* t 3.0))))
264.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log1p (expm1 (/ 2.0 (* t 3.0)))))))
80.0ms	(/ (* z (sqrt (+ t a))) t)

simplify117.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	956	1905
1	4496	1574
2	5001	1521

prune665.0ms

Filtered

137 candidates to 104 candidates (75.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	138	4	142

Merged error: 0b

Counts

142 → 4

regimes524.0ms

Accuracy

0% (2.3b remaining)

Error of 2.7b against oracle of 0.4b and baseline of 2.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	28
1	41	28

end0.0ms

sample2.2s

Algorithm

intervals

Results

770.0ms	8000×	body	80	valid
735.0ms	8107×	body	80	nan