Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	201×	body	80	valid
8.0ms	24×	body	2560	valid
5.0ms	26×	body	1280	valid
4.0ms	97×	body	80	nan
2.0ms	13×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	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)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

67.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
44.0ms	(- (* b b) (* (* 3.0 a) c))
68.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune382.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- 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)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

67.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0)
8.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0)
39.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
63.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	350	901
1	1306	833
2	5001	813

prune424.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (cbrt 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)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
49×	`add-exp-log`
46×	`add-sqr-sqrt`
45×	`times-frac`
34×	`associate-r`
24×	`add-cube-cbrt`
20×	`prod-exp`
18×	`cbrt-prod` `add-cbrt-cube`
15×	`div-exp`
14×	`distribute-lft-out`
10×	`add-log-exp`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`pow1` `cbrt-undiv` `distribute-rgt-neg-in` `associate-l`
4×	`rec-exp` `1-exp`
3×	`sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `div-inv`
1×	`+-commutative` `neg-sub0` `frac-times` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 124

Calls

4 calls:

137.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (cbrt 3.0)))
8.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (cbrt 3.0)))
49.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
61.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify83.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	699	1838
1	3493	1575
2	5002	1496

prune592.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 5.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

46.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
8.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
44.0ms	(- (* b b) (* (* 3.0 a) c))
67.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	368	755
1	1544	656
2	5002	644

prune332.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 5.1b

regimes674.0ms

Accuracy

89.1% (3.2b remaining)

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

bsearch230.0ms

Steps

Iters	Range	Point
10	3.61186574816217e+49	1.3635073763102398e+60	6.904457077194946e+59
5	1.2861463606709647e-114	3.883734753051949e-114	1.3066005810377465e-114
9	-4.1040688307943556e+139	-6.979584818812154e+133	-9.129564674001255e+133

Iters

Range

Point

3.61186574816217e+49

1.3635073763102398e+60

6.904457077194946e+59

1.2861463606709647e-114

3.883734753051949e-114

1.3066005810377465e-114

-4.1040688307943556e+139

-6.979584818812154e+133

-9.129564674001255e+133

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	33
1	55	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

287.0ms	1078×	body	2560	valid
258.0ms	5774×	body	80	valid
195.0ms	914×	body	1280	valid
136.0ms	3053×	body	80	nan
85.0ms	483×	body	640	valid
40.0ms	114×	body	5120	valid
36.0ms	269×	body	320	valid
9.0ms	103×	body	160	valid