Details

sample282.0ms

Algorithm

intervals

Results

8.0ms	34×	body	2560	valid
6.0ms	188×	body	80	valid
5.0ms	30×	body	1280	valid
3.0ms	104×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

10.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
70.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753

prune300.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.0b

localize12.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.7b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.1b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
21×	`distribute-lft-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg` `associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 284

Calls

4 calls:

13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
140.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
170.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	919	5579
1	3918	4508
2	5001	4505

prune584.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize13.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.7b	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
162×	`times-frac`
118×	`add-cube-cbrt`
60×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
32×	`add-exp-log`
28×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
23×	`add-cbrt-cube`
21×	`distribute-lft-neg-in`
16×	`div-exp`
10×	`cbrt-undiv` `fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`prod-exp` `div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`1-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `neg-log` `associate-/r/` `associate-/l/`

Counts

4 → 258

Calls

4 calls:

11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
19.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
180.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
150.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify125.0ms

Algorithm

egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	986	4687
1	4287	3613
2	5001	3595

prune502.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
0.8b	(- (* b_2 b_2) (* a c))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
62×	`add-cube-cbrt`
61×	`prod-diff`
34×	`sqrt-prod`
33×	`times-frac`
32×	`add-exp-log`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
17×	`div-exp`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1` `1-exp` `associate-/r*`
6×	`pow1` `prod-exp`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `rec-exp` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `cbrt-unprod` `inv-pow`

Counts

4 → 184

Calls

4 calls:

12.0ms	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
32.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify86.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	702	3223
1	2725	2180
2	5001	2099

prune276.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

regimes156.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.6b

bsearch144.0ms

Steps

Iters	Range	Point
9	1.846147638884188e+104	1.7844061428947563e+109	4.3957752798560445e+108
8	-1.0308405028667604e-278	-9.93812268464695e-282	-1.2249666784418393e-279
9	-3.3506371122085595e+158	-5.17073721832495e+150	-9.268713688859225e+150

Iters

Range

Point

1.846147638884188e+104

1.7844061428947563e+109

4.3957752798560445e+108

-1.0308405028667604e-278

-9.93812268464695e-282

-1.2249666784418393e-279

-3.3506371122085595e+158

-5.17073721832495e+150

-9.268713688859225e+150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	31
1	44	31
2	44	31

end0.0ms

sample1.0s

Algorithm

intervals

Results

223.0ms	1107×	body	2560	valid
199.0ms	5877×	body	80	valid
138.0ms	876×	body	1280	valid
95.0ms	2996×	body	80	nan
54.0ms	420×	body	640	valid
31.0ms	119×	body	5120	valid
22.0ms	236×	body	320	valid
8.0ms	125×	body	160	valid