Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	39×	body	2560	valid
6.0ms	36×	body	1280	valid
6.0ms	165×	body	80	valid
3.0ms	86×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	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: 33.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.0b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
43.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune244.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.4b

localize16.0ms

Local error

Found 4 expressions with local error:

15.3b	(cbrt (* (* 3.0 a) c))
15.3b	(cbrt (* (* 3.0 a) c))
15.3b	(cbrt (* (* 3.0 a) c))
22.6b	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

5.0ms	(cbrt (* (* 3.0 a) c))
5.0ms	(cbrt (* (* 3.0 a) c))
5.0ms	(cbrt (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (* (* 3.0 a) c))
94.0ms	(cbrt (* (* 3.0 a) c))
91.0ms	(cbrt (* (* 3.0 a) c))
118.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	217	582
1	616	541
2	2127	513
3	5001	511

prune225.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.4b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

20×	`fma-def` `*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`pow1` `distribute-lft-neg-in` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 88

Calls

4 calls:

21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	234	668
1	888	610
2	3709	588
3	5001	584

prune355.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 14.4b

localize18.0ms

Local error

Found 4 expressions with local error:

17.5b	(+ (- b) (* (* (cbrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `flip-+`

Counts

4 → 76

Calls

4 calls:

6.0ms	(+ (- b) (* (* (cbrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (- b) (* (* (cbrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
64.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify130.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	253	934
1	986	739
2	4284	661
3	5001	660

prune298.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 14.3b

regimes241.0ms

Accuracy

95.8% (0.9b remaining)

Error of 13.1b against oracle of 12.2b and baseline of 33.9b

bsearch182.0ms

Steps

Iters	Range	Point
7	2.703506994090381e+152	2.308573696785045e+154	1.0331115085790278e+154
10	-1.748936198008001e-296	1.7693602656524167e-306	-5.981525506949877e-298
10	-2.699314103090194e+180	-2.227381996671495e+165	-2.272454186637281e+165

Iters

Range

Point

2.703506994090381e+152

2.308573696785045e+154

1.0331115085790278e+154

-1.748936198008001e-296

1.7693602656524167e-306

-5.981525506949877e-298

-2.699314103090194e+180

-2.227381996671495e+165

-2.272454186637281e+165

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	46
1	57	46
2	57	46

end0.0ms

sample1.1s

Algorithm

intervals

Results

221.0ms	5915×	body	80	valid
217.0ms	1025×	body	2560	valid
154.0ms	893×	body	1280	valid
99.0ms	2995×	body	80	nan
61.0ms	447×	body	640	valid
27.0ms	107×	body	5120	valid
21.0ms	210×	body	320	valid
7.0ms	103×	body	160	valid