Details

sample46.0ms

Algorithm

intervals

Results

7.0ms	33×	body	2560	valid
7.0ms	185×	body	80	valid
6.0ms	97×	body	80	nan
5.0ms	29×	body	1280	valid
3.0ms	19×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

67.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
23.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
68.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
60.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune234.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
0.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
128×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
75×	`add-cube-cbrt`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 164

Calls

4 calls:

68.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
26.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
70.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
38.0ms	(- (* b b) (* 4.0 (* a c)))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	678	2536
1	2558	2441
2	5001	2441

prune400.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ 1 a))
0.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
37×	`times-frac`
26×	`add-exp-log`
25×	`associate-l`
23×	`add-cube-cbrt`
16×	`add-cbrt-cube`
13×	`associate-r`
10×	`add-log-exp`
8×	`div-exp` `prod-exp` `distribute-lft-out--` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `distribute-rgt-neg-in` `cbrt-unprod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp` `div-inv`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 114

Calls

4 calls:

100.0ms	(* (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ 1 a))
40.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ 1 a))
65.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
63.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	635	1393
1	2486	1237
2	5002	1224

prune285.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (sqrt (- (* b b) (* 4.0 (* a c)))) 2.0) a)
1.2b	(- (* b b) (* 4.0 (* a c)))
6.2b	(- (/ (/ (- b) 2.0) a) (/ (/ (sqrt (- (* b b) (* 4.0 (* a c)))) 2.0) a))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite407.0ms

Algorithm

rewrite-expression-head

Rules

249×	`times-frac`
160×	`add-sqr-sqrt`
152×	`*-un-lft-identity`
108×	`add-cube-cbrt`
42×	`sqrt-prod`
22×	`associate-/l*` `distribute-lft-out--`
13×	`div-inv`
12×	`difference-of-squares`
9×	`add-exp-log` `distribute-rgt-neg-in` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1`
4×	`distribute-rgt-out--`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `frac-sub` `associate-/l/` `sub-div`

Counts

4 → 186

Calls

4 calls:

24.0ms	(/ (/ (sqrt (- (* b b) (* 4.0 (* a c)))) 2.0) a)
9.0ms	(- (* b b) (* 4.0 (* a c)))
355.0ms	(- (/ (/ (- b) 2.0) a) (/ (/ (sqrt (- (* b b) (* 4.0 (* a c)))) 2.0) a))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series316.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (/ (sqrt (- (* b b) (* 4.0 (* a c)))) 2.0) a)
41.0ms	(- (* b b) (* 4.0 (* a c)))
97.0ms	(- (/ (/ (- b) 2.0) a) (/ (/ (sqrt (- (* b b) (* 4.0 (* a c)))) 2.0) a))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify81.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	815	2753
1	2754	2668
2	5001	2668

prune688.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.2b

regimes164.0ms

Accuracy

87.7% (3.4b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 33.4b

bsearch145.0ms

Steps

Iters	Range	Point
10	8.043557394408689e+68	7.456819745307919e+79	7.351468977489713e+79
6	-1.1225096205495847e-135	-1.431991336365571e-136	-2.140616590220207e-136
7	-1.4822129583791218e-41	-7.172614597146714e-44	-1.4477224379208848e-41

Iters

Range

Point

8.043557394408689e+68

7.456819745307919e+79

7.351468977489713e+79

-1.1225096205495847e-135

-1.431991336365571e-136

-2.140616590220207e-136

-1.4822129583791218e-41

-7.172614597146714e-44

-1.4477224379208848e-41

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	32
1	50	32
2	50	32

end0.0ms

sample1.2s

Algorithm

intervals

Results

241.0ms	1070×	body	2560	valid
228.0ms	5935×	body	80	valid
156.0ms	857×	body	1280	valid
112.0ms	2993×	body	80	nan
64.0ms	425×	body	640	valid
33.0ms	121×	body	5120	valid
26.0ms	225×	body	320	valid
8.0ms	108×	body	160	valid