Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	197×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	90×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify11.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite24.0ms

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:

5.0ms	(* (* 3.0 a) c)
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
49.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	337	531
1	1440	479
2	5002	467

prune259.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
10.0b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

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

series273.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
82.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	279	732
1	1153	610
2	5001	597

prune304.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- b))
1.2b	(- (* b b) (* (* 3.0 a) c))
22.0b	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
2×	`flip3--` `sqrt-div` `flip--`
1×	`neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `pow1/3` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 63

Calls

4 calls:

2.0ms	(cbrt (- b))
4.0ms	(- (* b b) (* (* 3.0 a) c))
1.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt (- b))
50.0ms	(- (* b b) (* (* 3.0 a) c))
155.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (sqrt (- (* b b) (* (* 3.0 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify99.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	248	556
1	816	502
2	3444	487
3	5002	482

prune265.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.7b

localize19.0ms

Local error

Found 4 expressions with local error:

22.2b	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- 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))))))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

1.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- 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)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- 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))))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	177	813
1	589	736
2	2437	709
3	5002	670

prune306.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 10.7b

regimes332.0ms

Accuracy

86.6% (3.1b remaining)

Error of 15.1b against oracle of 12.0b and baseline of 34.9b

bsearch126.0ms

Steps

Iters	Range		Point
9	3.2956103981062554e-86	3.6842556330088986e-79	3.6227398529818415e-79
10	-5.288637106878427e+83	-2.355035228211621e+66	-2.4276688444363324e+79

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	28
1	36	28

end0.0ms

sample1.1s

Algorithm

intervals

Results

225.0ms	1081×	body	2560	valid
211.0ms	5782×	body	80	valid
163.0ms	927×	body	1280	valid
109.0ms	2977×	body	80	nan
60.0ms	451×	body	640	valid
27.0ms	104×	body	5120	valid
26.0ms	257×	body	320	valid
8.0ms	124×	body	160	valid