Details

sample47.0ms

Algorithm

intervals

Results

12.0ms	209×	body	80	valid
7.0ms	32×	body	1280	valid
6.0ms	25×	body	2560	valid
4.0ms	103×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.1b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(- (* b b) (* (* 3.0 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite50.0ms

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:

19.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
42.0ms	(- (* b b) (* (* 3.0 a) c))
93.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
90.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

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

prune259.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	89	13	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	13	103

Merged error: 3.6b

Counts

103 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

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:

5.0ms	(* (* 3.0 a) c)
4.0ms	(- (* 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)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
47.0ms	(- (* b b) (* (* 3.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
66.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune215.0ms

Filtered

92 candidates to 71 candidates (77.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	93	12	105

Merged error: 3.6b

Counts

105 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.4b	(- (* b b) (* 3.0 (* a c)))
0.5b	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
17.4b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite22.0ms

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-l` `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-r` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* 3.0 (* a c))
4.0ms	(- (* b b) (* 3.0 (* a c)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series216.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* 3.0 (* a c))
44.0ms	(- (* b b) (* 3.0 (* a c)))
80.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	330	529
1	1217	478
2	5001	467

prune213.0ms

Filtered

92 candidates to 71 candidates (77.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	92	12	104

Merged error: 3.6b

Counts

104 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3.0 a))
0.4b	(- (* b b) (* (* 3.0 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

4.0ms	(/ 1 (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ 1 (* 3.0 a))
44.0ms	(- (* b b) (* (* 3.0 a) c))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	368	554
1	1514	497
2	5002	477

prune207.0ms

Filtered

102 candidates to 74 candidates (72.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	102	12	114

Merged error: 3.6b

Counts

114 → 12

regimes402.0ms

Accuracy

88.5% (3.2b remaining)

Error of 9.0b against oracle of 5.8b and baseline of 33.8b

bsearch173.0ms

Steps

Iters	Range	Point
9	1.7536266209730185e+54	9.156208036690931e+61	4.04873413931206e+54
6	3.745078909076236e-129	1.5507371656878094e-128	3.8834158381682525e-129
9	-1.5770435612361704e+159	-6.635354719968133e+153	-1.2515051492553303e+154

Iters

Range

Point

1.7536266209730185e+54

9.156208036690931e+61

4.04873413931206e+54

3.745078909076236e-129

1.5507371656878094e-128

3.8834158381682525e-129

-1.5770435612361704e+159

-6.635354719968133e+153

-1.2515051492553303e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	29
1	51	29
2	51	29

end0.0ms

sample1.3s

Algorithm

intervals

Results

280.0ms	1054×	body	2560	valid
278.0ms	5867×	body	80	valid
194.0ms	896×	body	1280	valid
129.0ms	2925×	body	80	nan
77.0ms	459×	body	640	valid
33.0ms	104×	body	5120	valid
27.0ms	218×	body	320	valid
9.0ms	107×	body	160	valid