Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	37×	body	2560	valid
7.0ms	197×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	77×	body	80	nan
2.0ms	16×	body	640	valid
0.0ms	4×	body	160	valid
0.0ms	2×	body	320	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 32.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

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:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
43.0ms	(- (* b b) (* (* 3.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune302.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

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:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
47.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune287.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
0.6b	(- (* b b) (* (* 3.0 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite44.0ms

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:

22.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
47.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (62.0ms)

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

prune362.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 8.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (/ 1 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite40.0ms

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-l`
16×	`add-cbrt-cube`
13×	`associate-r`
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/` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 125

Calls

4 calls:

19.0ms	(* (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (/ 1 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (/ 1 a))
44.0ms	(- (* b b) (* (* 3.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	644	1347
1	2750	1185
2	5002	1164

prune354.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 8.0b

regimes401.0ms

Accuracy

88.1% (3.3b remaining)

Error of 9.1b against oracle of 5.8b and baseline of 33.9b

bsearch135.0ms

Steps

Iters	Range		Point
6	6254161.133583045	42925490.781275615	31296389.294779938
5	1.4848686600671973e-153	5.873735982633398e-153	4.6569086088577344e-153
10	-4.4721271386820616e+151	-9.712280864301115e+136	-1.1259751240381662e+137

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	32
1	62	32
2	62	32

end0.0ms

sample1.1s

Algorithm

intervals

Results

225.0ms	1046×	body	2560	valid
211.0ms	5939×	body	80	valid
142.0ms	853×	body	1280	valid
105.0ms	2866×	body	80	nan
59.0ms	441×	body	640	valid
28.0ms	111×	body	5120	valid
22.0ms	226×	body	320	valid
8.0ms	117×	body	160	valid