Details

sample80.0ms

Algorithm

intervals

Results

21.0ms	188×	body	80	valid
16.0ms	32×	body	2560	valid
10.0ms	25×	body	1280	valid
9.0ms	91×	body	80	nan
5.0ms	17×	body	640	valid
3.0ms	6×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

38.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series279.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune232.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/r*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

23.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	361	863
1	1479	768
2	5002	759

prune216.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

61.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
43.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857

prune220.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.7b	(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
16.1b	(- (pow b 2) (pow b 2))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-exp-log`
22×	`unpow-prod-down`
16×	`add-cube-cbrt` `difference-of-squares`
13×	`add-cbrt-cube`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--` `prod-exp` `add-log-exp`
8×	`distribute-lft-out--`
7×	`pow1` `associate-l`
4×	`div-exp` `cbrt-unprod`
3×	`flip3-+` `times-frac` `associate-r` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `sqrt-div` `1-exp` `associate-*r/` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `distribute-rgt-in` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-pow1` `pow1/2` `+-inverses` `diff-log` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

12.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
198.0ms	(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
14.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series158.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
1.0ms	(- (pow b 2) (pow b 2))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	663	841
1	5001	626

prune299.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

regimes173.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.1b

bsearch232.0ms

Steps

Iters	Range	Point
8	5.408584085660923e+89	1.6744273082514658e+93	9.707084530269415e+92
9	8.576105435740817e-275	2.0823221738669132e-266	1.391640372823256e-271
7	-1.2511146020293208e+129	-2.5570389401985865e+127	-3.270912095499513e+127

Iters

Range

Point

5.408584085660923e+89

1.6744273082514658e+93

9.707084530269415e+92

8.576105435740817e-275

2.0823221738669132e-266

1.391640372823256e-271

-1.2511146020293208e+129

-2.5570389401985865e+127

-3.270912095499513e+127

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	25
1	44	25

end0.0ms

sample2.3s

Algorithm

intervals

Results

574.0ms	5792×	body	80	valid
504.0ms	1041×	body	2560	valid
377.0ms	916×	body	1280	valid
265.0ms	2838×	body	80	nan
158.0ms	481×	body	640	valid
66.0ms	250×	body	320	valid
66.0ms	107×	body	5120	valid
19.0ms	107×	body	160	valid