Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	201×	body	80	valid
6.0ms	24×	body	2560	valid
5.0ms	26×	body	1280	valid
4.0ms	13×	body	640	valid
4.0ms	97×	body	80	nan
2.0ms	14×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
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` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

69.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
9.0ms	(- (* b b) (* (* 3.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
43.0ms	(- (* b b) (* (* 3.0 a) c))
73.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
63.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune467.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0)
0.6b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`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` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

65.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0)
9.0ms	(- (* b b) (* (* 3.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0)
40.0ms	(- (* b b) (* (* 3.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
66.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	383	974
1	1444	896
2	5001	873

prune504.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

104.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
12.0ms	(- (* b b) (* (* 3.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
40.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	510	1012
1	2306	857
2	5001	844

prune494.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
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` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

68.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
9.0ms	(- (* b b) (* (* 3.0 a) c))
26.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
48.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune427.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

regimes704.0ms

Accuracy

89.1% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 34.8b

bsearch185.0ms

Steps

Iters	Range	Point
10	3.61186574816217e+49	1.3635073763102398e+60	5.816343192570514e+54
5	1.2861463606709647e-114	3.883734753051949e-114	1.3066005810377465e-114
5	-1.9814052033532642e+127	-6.516541830281216e+126	-1.3484843980259491e+127

Iters

Range

Point

3.61186574816217e+49

1.3635073763102398e+60

5.816343192570514e+54

1.2861463606709647e-114

3.883734753051949e-114

1.3066005810377465e-114

-1.9814052033532642e+127

-6.516541830281216e+126

-1.3484843980259491e+127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	30
1	55	30
2	55	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

284.0ms	1078×	body	2560	valid
263.0ms	5774×	body	80	valid
207.0ms	914×	body	1280	valid
140.0ms	3053×	body	80	nan
84.0ms	483×	body	640	valid
40.0ms	114×	body	5120	valid
34.0ms	269×	body	320	valid
9.0ms	103×	body	160	valid