Details

sample287.0ms

Algorithm

intervals

Results

9.0ms	202×	body	80	valid
5.0ms	24×	body	2560	valid
5.0ms	27×	body	1280	valid
3.0ms	96×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite120.0ms

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

Counts

4 → 100

Calls

4 calls:

64.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
31.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753

prune460.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a)))))
20.1b	(sqrt (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a))))
54.1b	(fma (- c) a (* c a))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(+ (- b_2) (sqrt (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a)))))
37.0ms	(sqrt (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a))))
0.0ms	(fma (- c) a (* c a))

series210.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- (* b_2 b_2) (* a c))
82.0ms	(+ (- b_2) (sqrt (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a)))))
76.0ms	(sqrt (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a))))
24.0ms	(fma (- c) a (* c a))

simplify113.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	300	609
1	1074	568
2	4378	552
3	5001	542

prune466.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (- b_2) (sqrt (+ (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a))) (fma (- c) a (* c a)))))
20.1b	(sqrt (+ (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a))) (fma (- c) a (* c a))))
54.1b	(fma (- c) a (* c a))
54.1b	(fma (- c) a (* c a))

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def`
8×	`add-cube-cbrt` `add-log-exp`
5×	`pow1` `sqrt-prod` `distribute-lft-out`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in`
2×	`flip3-+` `sqrt-div` `sum-log` `flip-+` `fma-udef`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `hypot-def`

Counts

4 → 67

Calls

4 calls:

191.0ms	(+ (- b_2) (sqrt (+ (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a))) (fma (- c) a (* c a)))))
138.0ms	(sqrt (+ (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a))) (fma (- c) a (* c a))))
0.0ms	(fma (- c) a (* c a))
0.0ms	(fma (- c) a (* c a))

series215.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (- b_2) (sqrt (+ (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a))) (fma (- c) a (* c a)))))
83.0ms	(sqrt (+ (+ (- (* b_2 b_2) (* a c)) (fma (- c) a (* c a))) (fma (- c) a (* c a))))
21.0ms	(fma (- c) a (* c a))
21.0ms	(fma (- c) a (* c a))

simplify112.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	234	761
1	784	705
2	4147	686
3	5001	670

prune605.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.6b	(- (* b_2 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

85.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
29.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
52.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	479	898
1	2054	778
2	5001	731

prune428.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

regimes262.0ms

Accuracy

89.2% (3.2b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 34.7b

bsearch245.0ms

Steps

Iters	Range	Point
10	3.61186574816217e+49	1.3635073763102398e+60	1.2800598687756953e+53
6	2.8042826217254478e-101	1.1404586743069836e-100	2.8872373531630686e-101
9	-4.1040688307943556e+139	-6.979584818812154e+133	-5.099479003111951e+134

Iters

Range

Point

3.61186574816217e+49

1.3635073763102398e+60

1.2800598687756953e+53

2.8042826217254478e-101

1.1404586743069836e-100

2.8872373531630686e-101

-4.1040688307943556e+139

-6.979584818812154e+133

-5.099479003111951e+134

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	39
1	49	39
2	49	39

end0.0ms

sample1.1s

Algorithm

intervals

Results

239.0ms	1082×	body	2560	valid
225.0ms	5770×	body	80	valid
166.0ms	913×	body	1280	valid
107.0ms	3044×	body	80	nan
69.0ms	481×	body	640	valid
33.0ms	114×	body	5120	valid
28.0ms	267×	body	320	valid
8.0ms	108×	body	160	valid