Details

sample290.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
6.0ms	180×	body	80	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

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize11.0ms

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)))

rewrite84.0ms

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:

51.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series257.0ms

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))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (46.0ms)

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

prune347.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

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)))

rewrite34.0ms

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:

16.0ms	(- (- 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)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify53.0ms

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

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

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)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.0ms	(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)))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt b_2)
32.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))
132.0ms	(fma (* (cbrt b_2) (cbrt b_2)) (- (cbrt b_2)) (- (sqrt (- (* b_2 b_2) (* a c)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	234	428
1	695	387
2	2409	369
3	5001	365

prune229.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* -1 b_2) (- (sqrt (- (* b_2 b_2) (* a c))))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.7b	(+ (* -1 b_2) (- (sqrt (- (* b_2 b_2) (* a c)))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

43.0ms	(/ (+ (* -1 b_2) (- (sqrt (- (* b_2 b_2) (* a c))))) a)
3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(+ (* -1 b_2) (- (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (+ (* -1 b_2) (- (sqrt (- (* b_2 b_2) (* a c))))) a)
32.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(+ (* -1 b_2) (- (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	410	885
1	1553	808
2	5002	787

prune258.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

regimes203.0ms

Accuracy

85.4% (4.2b remaining)

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

bsearch180.0ms

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	29
1	51	29
2	55	29
3	55	29

end0.0ms

sample997.0ms

Algorithm

intervals

Results

221.0ms	1094×	body	2560	valid
191.0ms	5857×	body	80	valid
146.0ms	917×	body	1280	valid
88.0ms	2907×	body	80	nan
53.0ms	419×	body	640	valid
27.0ms	102×	body	5120	valid
20.0ms	222×	body	320	valid
7.0ms	108×	body	160	valid