Details

sample10.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize4.0ms

Local error

Found 1 expressions with local error:

18.3b

(/ x (+ (* x x) 1.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

13.0ms

(/ x (+ (* x x) 1.0))

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(/ x (+ (* x x) 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	171	215
1	589	196
2	1979	191
3	5002	186

prune70.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1.0)))
0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
18.3b	(sqrt (+ (* x x) 1.0))
18.3b	(sqrt (+ (* x x) 1.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
30×	`sqrt-prod`
12×	`associate-/r*`
10×	`add-exp-log`
8×	`pow1` `sqrt-div` `add-cbrt-cube`
6×	`associate-/l*`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `sqrt-pow1` `pow1/2` `div-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `clear-num` `hypot-def` `div-inv`
1×	`rec-exp` `1-exp` `inv-pow`

Counts

4 → 128

Calls

4 calls:

14.0ms	(/ x (sqrt (+ (* x x) 1.0)))
17.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
10.0ms	(sqrt (+ (* x x) 1.0))
10.0ms	(sqrt (+ (* x x) 1.0))

series289.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ x (sqrt (+ (* x x) 1.0)))
76.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
41.0ms	(sqrt (+ (* x x) 1.0))
47.0ms	(sqrt (+ (* x x) 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	409	1002
1	1606	916
2	5001	867

prune273.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
0.1b	(/ 1 (pow x 5))
0.3b	(/ 1 (pow x 3))
15.5b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

1934×	`times-frac`
1320×	`add-sqr-sqrt`
1236×	`*-un-lft-identity`
1171×	`add-cube-cbrt`
1000×	`prod-diff`
650×	`unpow-prod-down`
251×	`cube-prod`
238×	`sqr-pow`
79×	`cube-mult` `unpow3`
72×	`div-inv`
63×	`difference-of-squares`
25×	`fma-neg`
22×	`add-exp-log`
19×	`associate-/r*`
12×	`div-exp`
8×	`add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `fma-udef`

Counts

4 → 1250

Calls

4 calls:

0.0ms	(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
8.0ms	(/ 1 (pow x 5))
9.0ms	(/ 1 (pow x 3))
111.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
47.0ms	(/ 1 (pow x 5))
31.0ms	(/ 1 (pow x 3))
103.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify267.0ms

Algorithm

egg-herbie

Counts

1262 → 1262

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	2411	31677
1	5002	18173

prune455.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.7b	(/ x (fma (* 1.0 1.0) 1.0 (pow x 6)))
15.6b	(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
28.2b	(* (/ x (fma (* 1.0 1.0) 1.0 (pow x 6))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
36×	`pow-prod-up`
25×	`add-sqr-sqrt`
24×	`pow-prod-down`
23×	`add-exp-log` `add-cbrt-cube`
22×	`pow-sqr`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`pow-plus`
14×	`associate-l`
13×	`pow2`
10×	`prod-exp` `cbrt-unprod`
9×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`associate-+r+` `flip3-+` `associate-/r` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `sum-log` `-commutative` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `associate-+r-` `sub-neg` `fma-def` `frac-2neg` `distribute-lft-in` `diff-log` `swap-sqr` `prod-diff` `associate-*l/` `clear-num`

Counts

4 → 153

Calls

4 calls:

30.0ms	(* (* x x) (* x x))
5.0ms	(/ x (fma (* 1.0 1.0) 1.0 (pow x 6)))
39.0ms	(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
148.0ms	(* (/ x (fma (* 1.0 1.0) 1.0 (pow x 6))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

series433.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* x x) (* x x))
236.0ms	(/ x (fma (* 1.0 1.0) 1.0 (pow x 6)))
40.0ms	(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
120.0ms	(* (/ x (fma (* 1.0 1.0) 1.0 (pow x 6))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

simplify83.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	626	1253
1	2900	1030
2	5001	995

prune337.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes49.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.0b

bsearch64.0ms

Steps

Iters	Range		Point
9	41.96612619086958	53435221.69579046	373.9008368767135
9	-17398359074955834.0	-1873866393.190807	-38320489792.4941

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample238.0ms

Algorithm

intervals

Results

130.0ms

8000×

body

valid