Details

sample65.0ms

Algorithm

intervals

Results

17.0ms	182×	body	80	valid
14.0ms	38×	body	2560	valid
9.0ms	31×	body	1280	valid
5.0ms	66×	body	80	nan
3.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
0.0ms	3×	body	160	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite55.0ms

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:

3.0ms	(- (* b b) (* (* 3.0 a) c))
34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

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

prune269.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.7b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.0b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

15.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
42.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
25.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
140.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
170.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify150.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	825	5119
1	3738	3863
2	5001	3860

prune518.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.2b	(- (* b b) (* (* 3.0 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

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:

8.0ms	(* (* 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)
45.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
66.0ms	(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

prune228.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.2b	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite77.0ms

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:

3.0ms	(- (* b b) (* (* 3.0 a) c))
51.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
14.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b b) (* (* 3.0 a) c))
105.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify96.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (81.0ms)

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

prune330.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.8b

regimes427.0ms

Accuracy

87.7% (3.3b remaining)

Error of 9.3b against oracle of 6.0b and baseline of 32.8b

bsearch233.0ms

Steps

Iters	Range		Point
9	2.361395911149281e+44	1.9602768074088032e+49	8.091177282128157e+46
10	3.133963618116426e-134	3.101996799263977e-122	5.035586839884384e-134
8	-4.003837004793086e+154	-2.2826144912851317e+150	-9.196781153225343e+150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	29
1	49	29
2	49	29

end0.0ms

sample1.8s

Algorithm

intervals

Results

488.0ms	5834×	body	80	valid
410.0ms	1078×	body	2560	valid
266.0ms	856×	body	1280	valid
201.0ms	2697×	body	80	nan
114.0ms	463×	body	640	valid
44.0ms	96×	body	5120	valid
42.0ms	222×	body	320	valid
14.0ms	104×	body	160	valid