Details

sample53.0ms

Algorithm

intervals

Results

13.0ms	188×	body	80	valid
9.0ms	33×	body	2560	valid
6.0ms	97×	body	80	nan
6.0ms	26×	body	1280	valid
3.0ms	15×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	1×	body	5120	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

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:

36.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	404	891
1	1481	801
2	5001	796

prune250.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

59.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
43.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify60.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857

prune247.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

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:

37.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

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

prune256.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.7b	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
9.9b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
52×	`times-frac`
51×	`add-exp-log`
30×	`add-cube-cbrt` `associate-l`
27×	`add-cbrt-cube`
20×	`prod-exp` `difference-of-squares`
16×	`div-exp`
13×	`sqrt-prod` `distribute-lft-out`
10×	`distribute-lft-out--`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `associate-r`
6×	`associate-/r*` `add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `associate-/l*`
3×	`div-inv`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 152

Calls

4 calls:

18.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
69.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
26.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
180.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
210.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify115.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	764	2421
1	3716	2067
2	5001	2044

prune369.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

regimes269.0ms

Accuracy

87.9% (3.2b remaining)

Error of 8.9b against oracle of 5.8b and baseline of 31.9b

bsearch202.0ms

Steps

Iters	Range	Point
11	3.0336165705843857e+124	3.3022304128508224e+146	1.196023561019716e+130
7	-3.887135277911521e-201	-1.3006679339526332e-202	-1.3594640158513444e-202
8	-3.4877376356874454e+65	-1.2492516085962122e+63	-3.384055336270002e+63

Iters

Range

Point

3.0336165705843857e+124

3.3022304128508224e+146

1.196023561019716e+130

-3.887135277911521e-201

-1.3006679339526332e-202

-1.3594640158513444e-202

-3.4877376356874454e+65

-1.2492516085962122e+63

-3.384055336270002e+63

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	25
1	40	25

end0.0ms

sample1.6s

Algorithm

intervals

Results

413.0ms	5758×	body	80	valid
298.0ms	1056×	body	2560	valid
229.0ms	967×	body	1280	valid
196.0ms	2885×	body	80	nan
87.0ms	461×	body	640	valid
40.0ms	103×	body	5120	valid
33.0ms	223×	body	320	valid
12.0ms	116×	body	160	valid