Details

sample78.0ms

Algorithm

intervals

Results

18.0ms	33×	body	2560	valid
18.0ms	188×	body	80	valid
9.0ms	97×	body	80	nan
8.0ms	26×	body	1280	valid
4.0ms	15×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	79	18
2	136	18
3	161	18
4	173	18
5	177	18
6	177	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize123.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 63

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	246	646
1	890	606
2	3702	588
3	5001	584

prune318.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.1b

localize127.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
5.6b	(/ (* a c) b)
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
3.0ms	(/ (* a c) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
20.0ms	(/ (* a c) b)
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	450	689
1	2176	609
2	5001	607

prune363.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize131.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b	(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
3.9b	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
31×	`times-frac`
30×	`add-exp-log`
26×	`*-un-lft-identity`
23×	`add-cbrt-cube`
22×	`add-cube-cbrt` `associate-r`
11×	`cbrt-prod`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`pow1` `associate-l`
6×	`unswap-sqr`
4×	`sqrt-prod`
3×	`flip3--` `associate-/r*` `flip--` `div-inv`
2×	`sqrt-div` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 115

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms	(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
23.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
107.0ms	(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
58.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify93.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	746	1376
1	3751	1199
2	5002	1153

prune724.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize137.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b	(/ (* 2.0 c) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (cbrt (* (cbrt b) (cbrt b)))) (/ c (cbrt (cbrt b))))) (* 2 b)))
4.5b	(* (/ (/ a (* (cbrt b) (cbrt b))) (cbrt (* (cbrt b) (cbrt b)))) (/ c (cbrt (cbrt b))))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
109×	`times-frac`
57×	`cbrt-prod`
46×	`*-un-lft-identity`
42×	`add-cube-cbrt`
41×	`add-exp-log`
32×	`associate-l`
31×	`associate-r`
27×	`add-cbrt-cube`
20×	`unswap-sqr`
16×	`cbrt-undiv` `div-exp`
11×	`prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`pow1` `div-inv`
4×	`sqrt-prod`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sqrt-div` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 167

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
104.0ms	(/ (* 2.0 c) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (cbrt (* (cbrt b) (cbrt b)))) (/ c (cbrt (cbrt b))))) (* 2 b)))
49.0ms	(* (/ (/ a (* (cbrt b) (cbrt b))) (cbrt (* (cbrt b) (cbrt b)))) (/ c (cbrt (cbrt b))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
106.0ms	(/ (* 2.0 c) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (cbrt (* (cbrt b) (cbrt b)))) (/ c (cbrt (cbrt b))))) (* 2 b)))
56.0ms	(* (/ (/ a (* (cbrt b) (cbrt b))) (cbrt (* (cbrt b) (cbrt b)))) (/ c (cbrt (cbrt b))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1127	2943
1	5002	2675

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

regimes269.0ms

Accuracy

94.5% (0.8b remaining)

Error of 7.6b against oracle of 6.8b and baseline of 21.4b

bsearch277.0ms

Steps

Iters	Range		Point
11	3.0336165705843857e+124	3.3022304128508224e+146	6.59313689338047e+135
8	-1.8056024443611976e+113	-8.371467560022169e+109	-2.6679509116126358e+112

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	78
1	69	78

end0.0ms

sample2.1s

Algorithm

intervals

Results

567.0ms	5758×	body	80	valid
413.0ms	1056×	body	2560	valid
312.0ms	967×	body	1280	valid
258.0ms	2885×	body	80	nan
122.0ms	461×	body	640	valid
54.0ms	103×	body	5120	valid
46.0ms	223×	body	320	valid
17.0ms	116×	body	160	valid