Details

sample42.0ms

Algorithm

intervals

Results

8.0ms	33×	body	2560	valid
7.0ms	185×	body	80	valid
5.0ms	25×	body	1280	valid
3.0ms	97×	body	80	nan
3.0ms	17×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	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: 34.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

11.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune236.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	9	90

Merged error: 5.8b

Counts

90 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
1.0b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 164

Calls

4 calls:

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

series479.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
47.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	678	2536
1	2558	2441
2	5001	2441

prune402.0ms

Filtered

176 candidates to 113 candidates (64.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	172	4	176
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	177	8	185

Merged error: 5.8b

Counts

185 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ (/ 1 2.0) a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
62×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
43×	`associate-r`
41×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`add-log-exp`
7×	`pow1` `associate-l`
6×	`div-exp`
5×	`flip3--` `prod-exp` `sqrt-prod` `flip--`
4×	`div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `diff-log` `cbrt-unprod`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `-commutative`

Counts

4 → 121

Calls

4 calls:

23.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ (/ 1 2.0) a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ (/ 1 2.0) a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify87.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	706	1522
1	3438	1393
2	5002	1357

prune344.0ms

Filtered

133 candidates to 98 candidates (73.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	134	7	141

Merged error: 5.8b

Counts

141 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
15.3b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* a 2.0))
19.0b	(- (pow b 2) (pow b 2))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`unpow-prod-down`
19×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`add-cube-cbrt`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--` `add-log-exp`
5×	`pow1`
3×	`flip3--` `times-frac` `sqrt-prod` `flip--` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`associate-+l-` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `+-inverses` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* a 2.0))
8.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series124.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* a 2.0))
1.0ms	(- (pow b 2) (pow b 2))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify127.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	441	648
1	2509	510
2	5001	467

prune253.0ms

Filtered

110 candidates to 70 candidates (63.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	109	8	117

Merged error: 5.7b

Counts

117 → 8

regimes170.0ms

Accuracy

96% (1.0b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.4b

bsearch171.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	1.0673291895585486e+103
11	1.8145151230270015e-269	9.272403512084269e-250	1.6944972861664959e-264
6	-1.2994787762702041e+157	-3.0529494422842112e+156	-3.0812943354752785e+156

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

1.0673291895585486e+103

1.8145151230270015e-269

9.272403512084269e-250

1.6944972861664959e-264

-1.2994787762702041e+157

-3.0529494422842112e+156

-3.0812943354752785e+156

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	39	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

253.0ms	1054×	body	2560	valid
238.0ms	5924×	body	80	valid
177.0ms	898×	body	1280	valid
109.0ms	2939×	body	80	nan
65.0ms	438×	body	640	valid
32.0ms	113×	body	5120	valid
22.0ms	199×	body	320	valid
12.0ms	131×	body	160	valid