Details

sample68.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
17.0ms	250×	body	80	nan

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 3.5b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* t 3.0))
0.3b	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
1.9b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.4b	(/ (* z (sqrt (+ t a))) t)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity`
119×	`prod-diff`
80×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
62×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
60×	`times-frac`
29×	`distribute-lft-out`
26×	`frac-sub`
20×	`div-inv`
17×	`flip3--` `flip--`
16×	`add-exp-log` `frac-times` `add-cbrt-cube`
10×	`associate-*r/`
7×	`flip3-+` `fma-neg` `flip-+`
6×	`pow1` `associate-r` `add-log-exp`
5×	`sub-neg` `associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-l/` `associate--l+` `associate-/r` `log1p-expm1-u` `associate-/l*`
3×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 253

Calls

4 calls:

5.0ms	(/ 2.0 (* t 3.0))
19.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
23.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
7.0ms	(/ (* z (sqrt (+ t a))) t)

series329.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 2.0 (* t 3.0))
58.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
176.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
79.0ms	(/ (* z (sqrt (+ t a))) t)

simplify86.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1388	4547
1	5001	3794

prune1.1s

Filtered

265 candidates to 158 candidates (59.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	262	3	265
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	263	3	266

Merged error: 0.2b

Counts

266 → 3

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ t a)) t)
0.3b	(/ 2.0 (* t 3.0))
0.3b	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
2.8b	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-un-lft-identity`
60×	`add-sqr-sqrt`
56×	`prod-diff`
54×	`add-cube-cbrt`
48×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
19×	`distribute-lft-out`
16×	`sqrt-prod`
13×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv` `associate-/l*`
8×	`frac-times` `flip3--` `flip--`
6×	`pow1` `associate-r` `frac-sub`
5×	`associate-l`
4×	`expm1-log1p-u` `flip3-+` `associate-r/` `associate-/r` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
2×	`sub-neg` `frac-2neg` `sqrt-div` `associate-*l/` `prod-exp` `associate--l+` `clear-num` `cbrt-unprod` `associate-/l/` `difference-of-squares`
1×	`pow-prod-down` `*-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 181

Calls

4 calls:

6.0ms	(/ (sqrt (+ t a)) t)
5.0ms	(/ 2.0 (* t 3.0))
21.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
1.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (sqrt (+ t a)) t)
16.0ms	(/ 2.0 (* t 3.0))
61.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
207.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify109.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	894	2691
1	4025	2163
2	5001	2158

prune936.0ms

Filtered

193 candidates to 108 candidates (56.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	193	3	196

Merged error: 0.2b

Counts

196 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
1.9b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.4b	(/ (* z (sqrt (+ t a))) t)
30.1b	(cbrt (pow (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))) 3))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity`
119×	`prod-diff`
81×	`add-sqr-sqrt`
75×	`add-cube-cbrt`
62×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
57×	`times-frac`
46×	`frac-sub`
29×	`distribute-lft-out`
26×	`flip3--` `flip--`
24×	`frac-times`
19×	`div-inv`
16×	`cube-div` `cbrt-div`
14×	`associate-*r/`
12×	`cbrt-prod`
11×	`add-exp-log` `add-cbrt-cube`
10×	`flip3-+` `flip-+`
7×	`fma-neg`
6×	`pow1` `associate-r` `associate-*l/` `add-log-exp`
5×	`sub-neg` `associate-l`
4×	`expm1-log1p-u` `associate--l+` `log1p-expm1-u`
3×	`unpow-prod-down` `cube-prod` `associate-/r*` `distribute-lft-out--`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `difference-of-squares`
1×	`cube-mult` `frac-2neg` `pow1/3` `diff-log` `unpow3` `pow-prod-down` `clear-num` `-commutative` `rem-cbrt-cube` `associate-/l` `unswap-sqr` `sqr-pow`

Counts

4 → 269

Calls

4 calls:

19.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
27.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
8.0ms	(/ (* z (sqrt (+ t a))) t)
14.0ms	(cbrt (pow (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))) 3))

series507.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
182.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
79.0ms	(/ (* z (sqrt (+ t a))) t)
183.0ms	(cbrt (pow (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))) 3))

simplify92.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1624	5556
1	5001	4983

prune1.3s

Filtered

281 candidates to 169 candidates (60.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	281	3	284

Merged error: 0.2b

Counts

284 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* 2.0 (fma (/ z 1) (/ (sqrt (+ t a)) t) (- (fma a b (- (fma a c (* 0.8333333333333334 c))))))))
0.2b	(/ (sqrt (+ t a)) t)
0.8b	(fma a b (- (fma a c (* 0.8333333333333334 c))))
2.5b	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (fma a b (- (fma a c (* 0.8333333333333334 c))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
21×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `fma-udef` `log1p-expm1-u` `distribute-lft-out`
3×	`associate-/r*`
2×	`sqrt-div` `exp-sum` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `exp-prod` `exp-to-pow` `frac-2neg` `distribute-lft-in` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 81

Calls

4 calls:

2.0ms	(exp (* 2.0 (fma (/ z 1) (/ (sqrt (+ t a)) t) (- (fma a b (- (fma a c (* 0.8333333333333334 c))))))))
7.0ms	(/ (sqrt (+ t a)) t)
1.0ms	(fma a b (- (fma a c (* 0.8333333333333334 c))))
1.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (fma a b (- (fma a c (* 0.8333333333333334 c))))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(exp (* 2.0 (fma (/ z 1) (/ (sqrt (+ t a)) t) (- (fma a b (- (fma a c (* 0.8333333333333334 c))))))))
60.0ms	(/ (sqrt (+ t a)) t)
36.0ms	(fma a b (- (fma a c (* 0.8333333333333334 c))))
162.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (fma a b (- (fma a c (* 0.8333333333333334 c))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	398	845
1	1240	761
2	5001	731

prune411.0ms

Filtered

93 candidates to 67 candidates (72.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	93	3	96

Merged error: 0.2b

Counts

96 → 3

regimes270.0ms

Accuracy

0% (1.4b remaining)

Error of 2.2b against oracle of 0.8b and baseline of 2.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	18
1	45	18
2	45	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

600.0ms	8000×	body	80	valid
561.0ms	8019×	body	80	nan