Details

sample51.0ms

Algorithm

intervals

Results

11.0ms	28×	body	2560	valid
9.0ms	189×	body	80	valid
7.0ms	34×	body	1280	valid
4.0ms	92×	body	80	nan
3.0ms	16×	body	640	valid
2.0ms	7×	body	5120	valid
0.0ms	4×	body	160	valid
0.0ms	2×	body	320	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: 35.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b	(- (* b b) (* (* 3.0 a) c))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite58.0ms

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:

36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
67.0ms	(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

prune356.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b	(- (* b b) (* (* 3.0 a) c))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

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)
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 3.0 a) c)
89.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms	(- (* b b) (* (* 3.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (38.0ms)

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

prune238.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3.0 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b	(- (* b b) (* (* 3.0 a) c))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

4.0ms	(/ 1 (* 3.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (* 3.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
48.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	368	554
1	1514	497
2	5002	477

prune261.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b	(- (* b b) (* (* 3.0 a) c))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

56.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
49.0ms	(- (* b b) (* (* 3.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	645	1311
1	3129	1145
2	5001	1130

prune342.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

regimes420.0ms

Accuracy

85.3% (4.2b remaining)

Error of 10.1b against oracle of 5.9b and baseline of 34.2b

bsearch90.0ms

Steps

Iters	Range		Point
7	1.9426594712364374e-87	2.1051237392284573e-85	1.667046824505827e-85
8	-3.734333779790662e+128	-2.2987999557012895e+125	-5.238946631357967e+127

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

224.0ms	1050×	body	2560	valid
216.0ms	5876×	body	80	valid
163.0ms	905×	body	1280	valid
99.0ms	2862×	body	80	nan
62.0ms	459×	body	640	valid
26.0ms	98×	body	5120	valid
22.0ms	215×	body	320	valid
8.0ms	122×	body	160	valid