Details

sample43.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
14.0ms	254×	body	80	nan

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	21	7
1	41	6
2	69	6
3	95	6
4	125	6
5	140	6
6	142	6
7	142	6

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.0b	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

128×	`times-frac`
95×	`add-sqr-sqrt` `*-un-lft-identity`
67×	`add-cube-cbrt`
16×	`associate-/r*`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`flip3--` `div-sub` `associate-/r/` `flip--` `fma-udef`

Counts

3 → 142

Calls

3 calls:

0.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
12.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
2.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

series175.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
82.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
56.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	627	1691
1	2379	1609
2	5002	1609

prune356.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (- x 1.0))
0.2b	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `associate-r`
4×	`fma-def` `associate-*r/`
3×	`expm1-log1p-u` `times-frac` `associate-l` `associate-/r*` `sum-log` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l+` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 92

Calls

3 calls:

15.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
14.0ms	(* 6.0 (- x 1.0))
25.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series168.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
43.0ms	(* 6.0 (- x 1.0))
82.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify75.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	466	778
1	2126	572
2	5002	560

prune202.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.0b	(/ (- x 1.0) (/ (* (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0))
0.0b	(/ (* (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0)
0.3b	(* (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
56×	`times-frac`
50×	`*-un-lft-identity`
34×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow1`
18×	`sqrt-prod`
10×	`associate-/r*`
8×	`sqrt-pow1` `pow1/2` `swap-sqr` `div-inv` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `associate-l` `associate-/l*`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `prod-exp` `pow-sqr` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`pow2` `flip3--` `pow-plus` `sqrt-unprod` `div-sub` `rem-square-sqrt` `associate-/r/` `*-commutative` `flip--` `fma-udef`

Counts

4 → 153

Calls

4 calls:

0.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
14.0ms	(/ (- x 1.0) (/ (* (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0))
6.0ms	(/ (* (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0)
10.0ms	(* (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
87.0ms	(/ (- x 1.0) (/ (* (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0))
63.0ms	(/ (* (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0)
42.0ms	(* (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify109.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	557	1825
1	2654	1580
2	5002	1542

prune417.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.3b	(* (- x 1.0) (sqrt 6.0))
0.6b	(/ (* (- x 1.0) (sqrt 6.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) (sqrt 6.0)))
0.7b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) (sqrt 6.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
54×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
28×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `associate-r`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-l/` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 147

Calls

4 calls:

0.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
12.0ms	(* (- x 1.0) (sqrt 6.0))
12.0ms	(/ (* (- x 1.0) (sqrt 6.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) (sqrt 6.0)))
3.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) (sqrt 6.0))

series411.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
88.0ms	(* (- x 1.0) (sqrt 6.0))
182.0ms	(/ (* (- x 1.0) (sqrt 6.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) (sqrt 6.0)))
99.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) (sqrt 6.0))

simplify97.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	661	1595
1	3090	1423
2	5002	1382

prune438.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes47.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	11	6

end0.0ms

sample1.2s

Algorithm

intervals

Results

553.0ms	8000×	body	80	valid
448.0ms	8128×	body	80	nan