Details

sample55.0ms

Algorithm

intervals

Results

11.0ms	180×	body	80	valid
11.0ms	39×	body	2560	valid
8.0ms	35×	body	1280	valid
5.0ms	98×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

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: 33.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (* b b) (* (* 4.0 a) c))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

14.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
77.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5001	673

prune198.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 5.3b

Counts

83 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
3.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.4b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
20.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
227.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
278.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	637	2580
1	3184	2341
2	5001	2328

prune429.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	158	10	168

Merged error: 5.3b

Counts

168 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (* b b) (* (* 4.0 a) c))
15.5b	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`flip3--` `sqrt-prod` `flip--`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 72

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(- (* b b) (* (* 4.0 a) c))
228.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	486	952
1	2894	749
2	5002	741

prune198.0ms

Filtered

84 candidates to 58 candidates (69.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	85	9	94

Merged error: 5.3b

Counts

94 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
0.8b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (* b b) (* (* 4.0 a) c))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`add-log-exp`
7×	`div-exp` `associate-/r*`
5×	`pow1` `cbrt-undiv` `div-inv`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `prod-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `neg-log` `clear-num` `associate-/r/` `cbrt-unprod`

Counts

4 → 94

Calls

4 calls:

12.0ms	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
88.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	549	1186
1	2337	1074
2	5002	1074

prune259.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	3	3	6
Picked	0	1	1
Done	1	1	2
Total	107	8	115

Merged error: 5.3b

Counts

115 → 8

regimes177.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.4b

bsearch237.0ms

Steps

Iters	Range	Point
10	1.4182100026226751e+88	1.1634796338171106e+98	1.0100267697287914e+93
10	-1.907966459858268e-129	-3.039489316543787e-144	-3.100973882795572e-144
7	-3.394702059408153e+117	-4.3501158911079625e+115	-3.631154114249338e+116

Iters

Range

Point

1.4182100026226751e+88

1.1634796338171106e+98

1.0100267697287914e+93

-1.907966459858268e-129

-3.039489316543787e-144

-3.100973882795572e-144

-3.394702059408153e+117

-4.3501158911079625e+115

-3.631154114249338e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	27
1	48	27

end0.0ms

sample1.4s

Algorithm

intervals

Results

318.0ms	1057×	body	2560	valid
317.0ms	5923×	body	80	valid
219.0ms	871×	body	1280	valid
150.0ms	2904×	body	80	nan
86.0ms	437×	body	640	valid
40.0ms	112×	body	5120	valid
36.0ms	232×	body	320	valid
11.0ms	108×	body	160	valid

Details

sample55.0ms

simplify11.0ms

prune3.0ms

localize11.0ms

rewrite30.0ms

series323.0ms

simplify45.0ms

prune198.0ms

localize15.0ms

rewrite51.0ms

series622.0ms

simplify110.0ms

prune429.0ms

localize16.0ms

rewrite47.0ms

series452.0ms

simplify72.0ms

prune198.0ms

localize14.0ms

rewrite34.0ms

series374.0ms

simplify66.0ms

prune259.0ms

regimes177.0ms

bsearch237.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling