Details

sample278.0ms

Algorithm

intervals

Results

6.0ms	35×	body	2560	valid
6.0ms	191×	body	80	valid
5.0ms	35×	body	1280	valid
3.0ms	115×	body	80	nan
2.0ms	5×	body	160	valid
1.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	3×	body	320	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize11.0ms

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))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

73.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
29.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063

prune350.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.9b

localize17.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 141

Calls

4 calls:

32.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
54.0ms	(sqrt (- (* b_2 b_2) (* a c)))
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))
52.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	369	2603
1	1203	1735
2	5001	1648

prune348.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 141

Calls

4 calls:

29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
52.0ms	(sqrt (- (* b_2 b_2) (* a c)))
54.0ms	(sqrt (- (* b_2 b_2) (* a c)))
52.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	369	2603
1	1203	1735
2	5001	1648

prune364.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.9b

localize25.0ms

Local error

Found 4 expressions with local error:

23.7b	(sqrt (- (* b_2 b_2) (* a c)))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))
24.6b	(cbrt (- (* b_2 b_2) (* a c)))
24.6b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 64

Calls

4 calls:

11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
6.0ms	(cbrt (- (* b_2 b_2) (* a c)))
6.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (- (* b_2 b_2) (* a c)))
51.0ms	(sqrt (- (* b_2 b_2) (* a c)))
77.0ms	(cbrt (- (* b_2 b_2) (* a c)))
79.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	205	538
1	609	510
2	1942	504
3	5002	500

prune373.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.9b

regimes374.0ms

Accuracy

85% (4.3b remaining)

Error of 9.9b against oracle of 5.5b and baseline of 34.4b

bsearch78.0ms

Steps

Iters	Range		Point
9	1.7695728335377845e+74	3.738006738925262e+80	2.910803917041586e+80
8	-2.4986524154890664e-82	-7.620401823751653e-85	-2.4336717856540716e-82

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

199.0ms	1063×	body	2560	valid
191.0ms	5904×	body	80	valid
146.0ms	915×	body	1280	valid
95.0ms	2946×	body	80	nan
55.0ms	465×	body	640	valid
22.0ms	97×	body	5120	valid
17.0ms	192×	body	320	valid
8.0ms	122×	body	160	valid