Details

sample61.0ms

Algorithm

intervals

Results

16.0ms	40×	body	2560	valid
13.0ms	185×	body	80	valid
7.0ms	25×	body	1280	valid
5.0ms	22×	body	640	valid
5.0ms	72×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
47.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune278.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
5.6b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.3b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite80.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
42.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
25.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 3.0 a) c))
143.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
177.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify122.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	669	2663
1	3431	2412
2	5001	2406

prune445.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
5.6b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
11.3b	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
22.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
17.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series509.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* b b) (* (* 3.0 a) c))
194.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
177.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
81.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify127.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	714	2019
1	4679	1554
2	5001	1549

prune352.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`fma-def` `*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`pow1` `distribute-lft-neg-in` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 88

Calls

4 calls:

11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	234	668
1	888	610
2	3709	588
3	5001	584

prune345.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.6b

regimes429.0ms

Accuracy

81% (5.2b remaining)

Error of 10.8b against oracle of 5.6b and baseline of 33.1b

bsearch118.0ms

Steps

Iters	Range		Point
7	8.110884543447496e-120	2.7406551721974403e-118	2.70136217446186e-118
9	-4.598976243999122e+69	-2.027222800079687e+63	-2.968512005892858e+66

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms

sample1.8s

Algorithm

intervals

Results

431.0ms	5897×	body	80	valid
406.0ms	1095×	body	2560	valid
252.0ms	835×	body	1280	valid
185.0ms	2915×	body	80	nan
114.0ms	461×	body	640	valid
46.0ms	107×	body	5120	valid
42.0ms	235×	body	320	valid
13.0ms	105×	body	160	valid