Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	201×	body	80	valid
6.0ms	24×	body	2560	valid
5.0ms	26×	body	1280	valid
4.0ms	97×	body	80	nan
2.0ms	13×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite110.0ms

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:

66.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series269.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
39.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
64.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	854
1	1658	750
2	5001	735

prune455.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite91.0ms

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-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

45.0ms	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
24.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
61.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	400	830
1	1623	721
2	5002	704

prune465.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

39.0ms	(/ 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
39.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
63.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	392	978
1	1549	874
2	5001	836

prune474.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

20×	`fma-def` `*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`pow1` `distribute-lft-neg-in` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 88

Calls

4 calls:

22.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
59.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
63.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify107.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	233	670
1	889	610
2	3678	588
3	5001	584

prune732.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

regimes283.0ms

Accuracy

88.7% (3.3b remaining)

Error of 8.8b against oracle of 5.5b and baseline of 34.8b

bsearch195.0ms

Steps

Iters	Range	Point
10	3.61186574816217e+49	1.3635073763102398e+60	1.5392622649860187e+58
6	2.8042826217254478e-101	1.1404586743069836e-100	2.826972719711758e-101
5	-1.1878056610710861e+97	-3.0473552791360753e+96	-4.1614218427535572e+96

Iters

Range

Point

3.61186574816217e+49

1.3635073763102398e+60

1.5392622649860187e+58

2.8042826217254478e-101

1.1404586743069836e-100

2.826972719711758e-101

-1.1878056610710861e+97

-3.0473552791360753e+96

-4.1614218427535572e+96

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	30
1	48	30
2	48	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

283.0ms	1081×	body	2560	valid
260.0ms	5776×	body	80	valid
202.0ms	912×	body	1280	valid
131.0ms	3053×	body	80	nan
82.0ms	483×	body	640	valid
36.0ms	114×	body	5120	valid
33.0ms	268×	body	320	valid
9.0ms	103×	body	160	valid