Details

sample292.0ms

Algorithm

intervals

Results

9.0ms	37×	body	2560	valid
6.0ms	180×	body	80	valid
6.0ms	35×	body	1280	valid
3.0ms	110×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 (100.0%)

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: 33.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite129.0ms

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))
23.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- 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)))

simplify114.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 2 (76.0ms)

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

prune289.0ms

Filtered

333 candidates to 112 candidates (66.4%)

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: 5.1b

Counts

334 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
1.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite124.0ms

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:

30.0ms	(/ 1 (/ a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
21.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ 1 (/ a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
38.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify140.0ms

Algorithm

egg-herbie

Counts

415 → 415

Iterations

Useful iterations: 2 (93.0ms)

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

prune374.0ms

Filtered

415 candidates to 148 candidates (64.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	410	5	415
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	413	11	424

Merged error: 5.1b

Counts

424 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
34×	`sqrt-prod`
20×	`fma-def` `difference-of-squares`
14×	`unswap-sqr`
12×	`add-cube-cbrt` `add-log-exp`
8×	`distribute-rgt-neg-in` `associate-l` `distribute-lft-out--`
6×	`pow1` `distribute-lft-neg-in`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `swap-sqr` `sum-log` `*-commutative` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 116

Calls

4 calls:

26.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
28.0ms	(sqrt (- (* b_2 b_2) (* a c)))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	271	814
1	933	762
2	3508	746
3	5001	742

prune297.0ms

Filtered

128 candidates to 96 candidates (25.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	129	10	139

Merged error: 5.1b

Counts

139 → 10

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`associate-r`
12×	`*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`times-frac`
9×	`associate-*r/`
6×	`add-exp-log` `add-cbrt-cube`
4×	`associate-/l*`
3×	`pow1` `associate-l` `associate-/r*`
2×	`prod-exp` `clear-num` `un-div-inv` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `pow-prod-down` `*-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 44

Calls

1 calls:

10.0ms

(* -1/2 (/ c b_2))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(* -1/2 (/ c b_2))

simplify71.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	188	156
1	871	141
2	3487	141
3	5001	141

prune46.0ms

Filtered

47 candidates to 32 candidates (31.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	44	13	57

Merged error: 5.1b

Counts

57 → 13

regimes256.0ms

Accuracy

85% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 34.4b

bsearch102.0ms

Steps

Iters	Range		Point
9	2.9593950748212843e-63	2.4702945119117623e-58	3.075714862027618e-63
10	-5.223066032138611e+59	-9.249404424269967e+45	-1.8583482015417066e+59

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

229.0ms	1098×	body	2560	valid
199.0ms	5798×	body	80	valid
145.0ms	885×	body	1280	valid
88.0ms	2778×	body	80	nan
59.0ms	464×	body	640	valid
29.0ms	116×	body	5120	valid
24.0ms	249×	body	320	valid
7.0ms	117×	body	160	valid