Details

sample372.0ms

Algorithm

intervals

Results

9.0ms	42×	body	2560	valid
7.0ms	183×	body	80	valid
6.0ms	33×	body	1280	valid
5.0ms	90×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	2×	body	320	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: 35.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.3b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite123.0ms

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:

22.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
70.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
10.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(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

prune321.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
0.3b	(/ (- 0 (- b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.6b	(- (* b_2 b_2) (* a c))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
19×	`prod-diff`
18×	`times-frac`
13×	`sqrt-prod` `distribute-lft-out--`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `fma-neg` `flip--` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `sub0-neg` `pow1/2` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 116

Calls

4 calls:

19.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
161.0ms	(/ (- 0 (- b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
83.0ms	(/ (- 0 (- b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
30.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	498	1516
1	1821	1187
2	5002	1161

prune288.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
0.3b	(/ (- 0 (* 1 (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
0.6b	(- (* b_2 b_2) (* a c))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
19×	`prod-diff`
13×	`sqrt-prod`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `fma-neg` `flip--` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/` `difference-of-squares`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `sub0-neg` `pow1/2` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

21.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(/ (- 0 (* 1 (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
9.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
83.0ms	(/ (- 0 (* 1 (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
33.0ms	(- (* b_2 b_2) (* a c))
53.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	496	1447
1	1896	1097
2	5001	1090

prune288.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 67

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series197.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* b_2 b_2) (* a c))
54.0ms	(sqrt (- (* b_2 b_2) (* a c)))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	159	470
1	505	446
2	1688	440
3	5001	431

prune276.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.1b

regimes279.0ms

Accuracy

84.7% (4.4b remaining)

Error of 10.0b against oracle of 5.6b and baseline of 34.4b

bsearch84.0ms

Steps

Iters	Range		Point
10	2.2777662256792016e-86	1.8614563384609176e-67	1.2091207453430995e-70
6	-1.3854637168610187e+102	-1.5284190780878897e+101	-9.912439588753869e+101

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	15
1	44	15
2	44	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

237.0ms	1129×	body	2560	valid
211.0ms	5783×	body	80	valid
162.0ms	917×	body	1280	valid
102.0ms	2996×	body	80	nan
62.0ms	436×	body	640	valid
29.0ms	105×	body	5120	valid
23.0ms	224×	body	320	valid
8.0ms	117×	body	160	valid