Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	37×	body	2560	valid
6.0ms	179×	body	80	valid
6.0ms	35×	body	1280	valid
4.0ms	110×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	5×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 33.7b

Counts

2 → 1

localize14.0ms

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))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

139×	`add-sqr-sqrt`
116×	`*-un-lft-identity`
60×	`times-frac`
42×	`unswap-sqr`
36×	`add-cube-cbrt` `associate-l`
30×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`sqrt-prod`
18×	`associate-r`
14×	`distribute-rgt-neg-in`
12×	`associate-/r` `-commutative` `distribute-lft-out--`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`swap-sqr`
5×	`pow1` `associate-/l*`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`

Counts

4 → 178

Calls

4 calls:

43.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
24.0ms	(- (* b b) (* (* 3.0 a) c))
34.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
47.0ms	(- (* b b) (* (* 3.0 a) c))
85.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
80.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	612	2254
1	2407	2158
2	5001	2141

prune311.0ms

Filtered

190 candidates to 109 candidates (42.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	179	11	190
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	179	12	191

Merged error: 5.1b

Counts

191 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
40×	`unswap-sqr`
37×	`*-un-lft-identity`
33×	`associate-l`
30×	`difference-of-squares`
24×	`sqrt-prod`
12×	`distribute-lft-out--`
10×	`pow1` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
8×	`*-commutative`
6×	`swap-sqr` `associate-r`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `neg-log` `flip-+`

Counts

4 → 115

Calls

4 calls:

8.0ms	(* (* 3.0 a) c)
23.0ms	(- (* b b) (* (* 3.0 a) c))
37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* 3.0 a) c)
53.0ms	(- (* b b) (* (* 3.0 a) c))
88.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	399	924
1	1487	883
2	5001	869

prune214.0ms

Filtered

127 candidates to 76 candidates (40.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	127	12	139

Merged error: 5.1b

Counts

139 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
48×	`sqrt-prod`
38×	`*-un-lft-identity`
36×	`unswap-sqr`
30×	`difference-of-squares`
18×	`associate-l`
12×	`distribute-lft-out--` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `swap-sqr` `*-commutative`
4×	`add-exp-log` `sqrt-div` `sum-log` `add-cbrt-cube` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 102

Calls

4 calls:

35.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
38.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
27.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify132.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	284	1054
1	945	1012
2	3750	996
3	5001	980

prune322.0ms

Filtered

114 candidates to 72 candidates (36.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	114	12	126

Merged error: 5.1b

Counts

126 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

145×	`add-sqr-sqrt`
72×	`sqrt-prod`
54×	`unswap-sqr`
47×	`*-un-lft-identity`
45×	`difference-of-squares`
27×	`associate-l`
18×	`distribute-lft-out--`
9×	`swap-sqr` `*-commutative`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `flip-+`

Counts

4 → 123

Calls

4 calls:

37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
27.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
78.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify139.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	284	1245
1	945	1222
2	3750	1210
3	5001	1188

prune337.0ms

Filtered

135 candidates to 78 candidates (42.2%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	135	12	147

Merged error: 5.1b

Counts

147 → 12

regimes498.0ms

Accuracy

85.5% (4.2b remaining)

Error of 9.7b against oracle of 5.5b and baseline of 34.4b

bsearch99.0ms

Steps

Iters	Range		Point
9	2.9593950748212843e-63	2.4702945119117623e-58	1.9850830413571982e-59
6	-6.52330204454965e+152	-1.537752741313912e+152	-1.8283521702272678e+152

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

238.0ms	1098×	body	2560	valid
211.0ms	5795×	body	80	valid
156.0ms	885×	body	1280	valid
95.0ms	2780×	body	80	nan
64.0ms	465×	body	640	valid
31.0ms	116×	body	5120	valid
25.0ms	249×	body	320	valid
8.0ms	118×	body	160	valid