Details

sample65.0ms

Algorithm

intervals

Results

9.0ms	185×	body	80	valid
9.0ms	29×	body	2560	valid
7.0ms	29×	body	1280	valid
4.0ms	81×	body	80	nan
3.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	3×	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

prune4.0ms

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: 31.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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:

13.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune155.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	8	90

Merged error: 4.1b

Counts

90 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

14.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	538	1801
1	2573	1602
2	5002	1528

prune147.0ms

Filtered

73 candidates to 137 candidates (-87.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	138	7	145

Merged error: 4.1b

Counts

145 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.8b	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
14.6b	(- (pow b 2) (pow b 2))
18.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`unpow-prod-down`
19×	`add-exp-log`
16×	`difference-of-squares`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--` `add-log-exp`
8×	`distribute-lft-out--`
7×	`div-exp`
5×	`pow1` `associate-/l/`
4×	`cbrt-undiv` `prod-exp`
3×	`flip3-+` `times-frac` `associate-/r*` `sqrt-prod` `flip-+`
2×	`frac-times` `flip3--` `sqrt-div` `associate-*r/` `sum-log` `flip--` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `+-inverses` `diff-log` `1-exp` `neg-log` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 107

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
8.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
1.0ms	(- (pow b 2) (pow b 2))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify204.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (194.0ms)

Iter	Nodes	Cost
0	590	805
1	4021	571
2	5001	552

prune207.0ms

Filtered

79 candidates to 119 candidates (-50.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	118	8	126

Merged error: 4.1b

Counts

126 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 c) (/ 1 (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.3b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
26×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube`
15×	`add-sqr-sqrt` `times-frac`
14×	`add-cube-cbrt`
12×	`prod-exp`
10×	`pow1` `add-log-exp`
8×	`distribute-lft-out`
6×	`cbrt-unprod`
4×	`distribute-rgt-neg-in` `div-exp`
3×	`pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `rec-exp` `flip3--` `flip3-+` `sqrt-div` `1-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

18.0ms	(* (* 2.0 c) (/ 1 (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* 2.0 c) (/ 1 (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	507	953
1	2373	795
2	5001	767

prune119.0ms

Filtered

65 candidates to 100 candidates (-53.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	100	8	108

Merged error: 4.1b

Counts

108 → 8

regimes383.0ms

Accuracy

87.5% (3.5b remaining)

Error of 9.6b against oracle of 6.1b and baseline of 34.1b

bsearch106.0ms

Steps

Iters	Range	Point
9	1.2602211262179521e+138	8.859133655848229e+145	8.705825951030607e+140
8	-4.8997346531216295e-144	-5.794541442575482e-147	-1.0782197627274848e-144
9	-9.60502816356221e-23	-6.201396514114901e-29	-9.072891879288944e-23

Iters

Range

Point

1.2602211262179521e+138

8.859133655848229e+145

8.705825951030607e+140

-4.8997346531216295e-144

-5.794541442575482e-147

-1.0782197627274848e-144

-9.60502816356221e-23

-6.201396514114901e-29

-9.072891879288944e-23

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	31
1	50	31

end0.0ms

sample1.5s

Algorithm

intervals

Results

317.0ms	1046×	body	2560	valid
315.0ms	5957×	body	80	valid
223.0ms	900×	body	1280	valid
134.0ms	2670×	body	80	nan
89.0ms	458×	body	640	valid
35.0ms	91×	body	5120	valid
29.0ms	202×	body	320	valid
12.0ms	101×	body	160	valid

Details

sample65.0ms

simplify14.0ms

prune4.0ms

localize12.0ms

rewrite31.0ms

series63.0ms

simplify46.0ms

prune155.0ms

localize14.0ms

rewrite35.0ms

series75.0ms

simplify71.0ms

prune147.0ms

localize20.0ms

rewrite49.0ms

series35.0ms

simplify204.0ms

prune207.0ms

localize13.0ms

rewrite37.0ms

series95.0ms

simplify65.0ms

prune119.0ms

regimes383.0ms

bsearch106.0ms

simplify2.0ms

end0.0ms

sample1.5s

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