Details

sample277.0ms

Algorithm

intervals

Results

7.0ms	36×	body	2560	valid
6.0ms	192×	body	80	valid
4.0ms	83×	body	80	nan
4.0ms	26×	body	1280	valid
1.0ms	12×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	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: 31.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

235×	`add-sqr-sqrt`
180×	`prod-diff`
164×	`*-un-lft-identity`
128×	`add-cube-cbrt`
92×	`associate-l`
84×	`associate-r`
43×	`swap-sqr`
42×	`unswap-sqr`
32×	`*-commutative`
20×	`difference-of-squares`
17×	`sqrt-prod`
15×	`times-frac` `fma-neg`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 321

Calls

4 calls:

30.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	839	3943
1	2852	2600
2	5002	2492

prune297.0ms

Filtered

333 candidates to 112 candidates (33.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	324	9	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	325	9	334

Merged error: 4.5b

Counts

334 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.2b	(- (* b_2 b_2) (* a c))
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

285×	`add-sqr-sqrt`
251×	`*-un-lft-identity`
180×	`prod-diff`
178×	`add-cube-cbrt`
123×	`times-frac`
92×	`associate-l`
84×	`associate-r`
43×	`swap-sqr`
42×	`unswap-sqr`
32×	`*-commutative`
28×	`distribute-lft-out`
26×	`associate-/r*`
20×	`difference-of-squares`
19×	`associate-/r/`
17×	`distribute-rgt-neg-in` `sqrt-prod`
15×	`add-exp-log` `fma-neg`
10×	`fma-def` `add-log-exp`
9×	`add-cbrt-cube`
8×	`distribute-lft-out--`
7×	`div-exp` `associate-/l*`
6×	`pow1`
5×	`flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `distribute-lft-neg-in` `clear-num`
2×	`rec-exp` `flip3--` `frac-2neg` `sqrt-div` `1-exp` `sum-log` `flip--` `remove-double-div`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `inv-pow`

Counts

4 → 403

Calls

4 calls:

31.0ms	(/ 1 (/ a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
22.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ 1 (/ a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
36.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

415 → 415

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	1031	5118
1	4111	3608
2	5001	3603

prune377.0ms

Filtered

415 candidates to 148 candidates (35.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	409	6	415
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	416	8	424

Merged error: 4.5b

Counts

424 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

235×	`add-sqr-sqrt`
180×	`prod-diff`
164×	`*-un-lft-identity`
128×	`add-cube-cbrt`
92×	`associate-l`
84×	`associate-r`
43×	`swap-sqr`
42×	`unswap-sqr`
32×	`*-commutative`
20×	`difference-of-squares`
17×	`sqrt-prod`
15×	`times-frac` `fma-neg`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 321

Calls

4 calls:

29.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
29.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	839	3943
1	2852	2600
2	5002	2492

prune258.0ms

Filtered

333 candidates to 110 candidates (33.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	333	0	333
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	333	8	341

Merged error: 4.5b

Counts

341 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (+ (- b_2) (sqrt (fma (* b_2 1) b_2 (- (* c a)))))))
0.3b	(fma (* b_2 1) b_2 (- (* c a)))
0.5b	(+ (- b_2) (sqrt (fma (* b_2 1) b_2 (- (* c a)))))
20.5b	(sqrt (fma (* b_2 1) b_2 (- (* c a))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

125×	`*-un-lft-identity`
123×	`times-frac`
69×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
28×	`distribute-lft-out`
26×	`associate-/r*`
19×	`associate-/r/`
17×	`distribute-rgt-neg-in`
15×	`add-exp-log`
10×	`fma-def`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp` `associate-/l*`
6×	`pow1`
5×	`flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `distribute-lft-neg-in` `clear-num` `sqrt-prod`
2×	`rec-exp` `frac-2neg` `1-exp` `sum-log` `remove-double-div`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `neg-log` `fma-udef` `inv-pow`

Counts

4 → 174

Calls

4 calls:

13.0ms	(/ 1 (/ a (+ (- b_2) (sqrt (fma (* b_2 1) b_2 (- (* c a)))))))
1.0ms	(fma (* b_2 1) b_2 (- (* c a)))
7.0ms	(+ (- b_2) (sqrt (fma (* b_2 1) b_2 (- (* c a)))))
2.0ms	(sqrt (fma (* b_2 1) b_2 (- (* c a))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ 1 (/ a (+ (- b_2) (sqrt (fma (* b_2 1) b_2 (- (* c a)))))))
44.0ms	(fma (* b_2 1) b_2 (- (* c a)))
84.0ms	(+ (- b_2) (sqrt (fma (* b_2 1) b_2 (- (* c a)))))
76.0ms	(sqrt (fma (* b_2 1) b_2 (- (* c a))))

simplify74.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	517	2170
1	2410	1962
2	5001	1849

prune296.0ms

Filtered

186 candidates to 114 candidates (61.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	182	4	186
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	185	9	194

Merged error: 4.5b

Counts

194 → 9

regimes255.0ms

Accuracy

83.2% (4.6b remaining)

Error of 10.5b against oracle of 5.9b and baseline of 33.3b

bsearch86.0ms

Steps

Iters	Range		Point
6	5.170278655164064e-52	2.1804079894200568e-51	1.2688336265881624e-51
10	-2.7851241427016145e+159	-9.354797223898085e+144	-1.063633977705377e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample969.0ms

Algorithm

intervals

Results

200.0ms	5954×	body	80	valid
196.0ms	1028×	body	2560	valid
131.0ms	853×	body	1280	valid
93.0ms	2983×	body	80	nan
55.0ms	466×	body	640	valid
22.0ms	220×	body	320	valid
21.0ms	88×	body	5120	valid
6.0ms	101×	body	160	valid