Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	180×	body	80	valid
6.0ms	35×	body	2560	valid
4.0ms	29×	body	1280	valid
3.0ms	88×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	5×	body	5120	valid
0.0ms	7×	body	160	valid
0.0ms	3×	body	320	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

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:

46.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (47.0ms)

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

prune338.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

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:

17.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (34.0ms)

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

prune347.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- b_2))
1.0b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.8b	(fma (* (cbrt (- b_2)) (cbrt (- b_2))) (cbrt (- b_2)) (- (sqrt (- (* b_2 b_2) (* a c)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
2×	`flip3--` `sqrt-div` `flip--`
1×	`neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `pow1/3` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 63

Calls

4 calls:

2.0ms	(cbrt (- b_2))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
0.0ms	(fma (* (cbrt (- b_2)) (cbrt (- b_2))) (cbrt (- b_2)) (- (sqrt (- (* b_2 b_2) (* a c)))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (- b_2))
32.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))
168.0ms	(fma (* (cbrt (- b_2)) (cbrt (- b_2))) (cbrt (- b_2)) (- (sqrt (- (* b_2 b_2) (* a c)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	238	505
1	668	455
2	2215	439
3	5003	435

prune256.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (- (sqrt (- (* b_2 b_2) (* a c))))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.7b	(+ (- b_2) (- (sqrt (- (* b_2 b_2) (* a c)))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
30×	`distribute-lft-out`
27×	`times-frac`
23×	`add-sqr-sqrt` `distribute-rgt-neg-in`
22×	`add-cube-cbrt`
14×	`add-log-exp`
13×	`distribute-lft-neg-in`
11×	`neg-mul-1`
10×	`fma-def`
9×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`neg-sub0` `expm1-log1p-u` `div-sub` `neg-log` `sum-log` `log1p-expm1-u`
3×	`associate-/r*` `sqrt-prod`
2×	`associate-+l-` `associate-+r-` `distribute-neg-out` `flip3--` `flip3-+` `sqrt-div` `unsub-neg` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `distribute-frac-neg` `div-exp` `prod-diff` `clear-num` `div-inv`

Counts

4 → 130

Calls

4 calls:

67.0ms	(/ (+ (- b_2) (- (sqrt (- (* b_2 b_2) (* a c))))) a)
3.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(+ (- b_2) (- (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (+ (- b_2) (- (sqrt (- (* b_2 b_2) (* a c))))) a)
32.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(+ (- b_2) (- (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	425	1135
1	1655	1029
2	5002	1012

prune281.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

regimes248.0ms

Accuracy

85.4% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 34.0b

bsearch174.0ms

Steps

Iters	Range		Point
6	4.706455236749836e+29	5.491842449186372e+30	5.349311795482947e+30
10	-9.63247495909049e-100	-1.4236932931255447e-118	-4.052378358256912e-102
7	-2.3555604230285885e-90	-2.5832717791734895e-92	-8.212187268803771e-92
10	-6.255678465194574e+71	-1.2356841275142139e+58	-1.0366436397824178e+68

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	30
1	51	30
2	51	30

end0.0ms

sample999.0ms

Algorithm

intervals

Results

207.0ms	1094×	body	2560	valid
193.0ms	5857×	body	80	valid
149.0ms	917×	body	1280	valid
96.0ms	2907×	body	80	nan
50.0ms	419×	body	640	valid
27.0ms	102×	body	5120	valid
20.0ms	222×	body	320	valid
7.0ms	108×	body	160	valid