Details

sample35.0ms

Algorithm

intervals

Results

16.0ms	285×	body	80	valid
4.0ms	84×	body	80	nan

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	80	18
2	143	18
3	177	18
4	189	18
5	193	18
6	193	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize117.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
37×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
8×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 151

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	418	3056
1	1471	2008
2	5001	1917

prune435.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

localize115.0ms

Local error

Found 4 expressions with local error:

9.8b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.5b	(sqrt (- (* b b) (* (* 4.0 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) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	249	756
1	969	641
2	4038	626
3	5001	624

prune395.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.9b

localize123.0ms

Local error

Found 4 expressions with local error:

23.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
91.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
93.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	161	680
1	548	636
2	2229	628
3	5001	628

prune473.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.9b

localize118.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
4.8b	(/ (* a c) b)
22.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
60×	`prod-diff`
55×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
34×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`times-frac` `associate-/r*` `add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `distribute-lft-out`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 159

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
3.0ms	(/ (* a c) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
172.0ms	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
18.0ms	(/ (* a c) b)
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	610	3137
1	2564	2048
2	5001	1968

prune410.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

regimes187.0ms

Accuracy

91.5% (1.1b remaining)

Error of 7.7b against oracle of 6.6b and baseline of 20.1b

bsearch145.0ms

Steps

Iters	Range		Point
6	1.1594993669073426e+93	1.3006782908792091e+94	7.866463199287323e+93
9	-1.2845883854340997e+78	-5.15156631625478e+72	-1.0088663643419234e+78

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	59
1	57	59

end0.0ms

sample875.0ms

Algorithm

intervals

Results

483.0ms	8682×	body	80	valid
147.0ms	2947×	body	80	nan