Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	42×	body	2560	valid
7.0ms	183×	body	80	valid
5.0ms	30×	body	1280	valid
3.0ms	90×	body	80	nan
2.0ms	18×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	2×	body	320	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.6b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`associate-r` `pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `flip--` `associate-/l/`
1×	`neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `div-sub` `associate-l` `prod-diff` `clear-num` `associate-/r` `-commutative` `flip-+` `div-inv`

Counts

4 → 83

Calls

4 calls:

17.0ms	(* (* 4.0 a) c)
66.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (* 4.0 a) c)
95.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.0ms	(- (* b b) (* (* 4.0 a) c))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	460	740
1	1973	650
2	5002	641

prune252.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
0.6b	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) (* 2.0 a))
0.6b	(- (* b b) (pow (* 4.0 (* a c)) 1))
26.1b	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

28.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
84.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) (* 2.0 a))
10.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
16.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
93.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) (* 2.0 a))
39.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
63.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

simplify64.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	493	1080
1	1913	899
2	5001	887

prune303.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) a)
0.6b	(- (* b b) (pow (* 4.0 (* a c)) 1))
26.1b	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `prod-diff` `sqrt-prod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-lft-neg-in` `associate-/r*` `sqr-pow`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `unpow-prod-down` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

30.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
82.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) a)
10.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
16.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
88.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) a)
39.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
63.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

simplify61.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	457	1217
1	1762	1062
2	5002	1043

prune354.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))))
0.3b	(/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))))
0.6b	(- (* b b) (pow (* 4.0 (* a c)) 1))
26.1b	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity` `times-frac`
77×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
32×	`distribute-lft-out`
26×	`associate-/r*`
17×	`add-exp-log`
16×	`distribute-rgt-neg-in`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
5×	`flip3-+` `prod-diff` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`sqr-pow`
2×	`rec-exp` `flip3--` `frac-2neg` `sqrt-div` `1-exp` `clear-num` `flip--`
1×	`sub-neg` `unpow-prod-down` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `inv-pow`

Counts

4 → 190

Calls

4 calls:

57.0ms	(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))))
51.0ms	(/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))))
10.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
18.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))))
171.0ms	(/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))))
42.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
60.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

simplify96.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	643	2897
1	3105	2536
2	5002	2419

prune390.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.1b

regimes298.0ms

Accuracy

84.7% (4.4b remaining)

Error of 10.0b against oracle of 5.6b and baseline of 34.4b

bsearch108.0ms

Steps

Iters	Range		Point
10	2.2777662256792016e-86	1.8614563384609176e-67	1.2091207453430995e-70
6	-1.3854637168610187e+102	-1.5284190780878897e+101	-9.912439588753869e+101

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	19
1	40	19

end0.0ms

sample1.2s

Algorithm

intervals

Results

244.0ms	1127×	body	2560	valid
215.0ms	5786×	body	80	valid
159.0ms	916×	body	1280	valid
107.0ms	2998×	body	80	nan
64.0ms	438×	body	640	valid
27.0ms	105×	body	5120	valid
23.0ms	222×	body	320	valid
8.0ms	117×	body	160	valid