Details

sample40.0ms

Algorithm

intervals

Results

11.0ms	32×	body	2560	valid
6.0ms	182×	body	80	valid
5.0ms	28×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	10×	body	640	valid
0.0ms	4×	body	320	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	40	9
2	48	9
3	50	9
4	52	9
5	53	9
6	53	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.1b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 92

Calls

4 calls:

26.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
24.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	297	948
1	884	898
2	2732	885
3	5001	883

prune306.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ 1.0 (cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))
0.1b	(pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.3b	(cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
62×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
54×	`cbrt-prod`
48×	`unpow-prod-down` `cube-prod`
39×	`sqrt-prod`
10×	`sqrt-div`
8×	`associate-/r/`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `fma-def`
2×	`cube-div` `cube-mult` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `cbrt-div` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `sum-log` `rem-cbrt-cube` `distribute-lft-out`

Counts

4 → 170

Calls

4 calls:

63.0ms	(+ 1.0 (cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))
16.0ms	(pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.0ms	(cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))

series511.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(+ 1.0 (cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))
116.0ms	(pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
67.0ms	(cbrt (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))

simplify70.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	570	2241
1	2477	1968
2	5003	1866

prune374.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.3b

localize16.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
4.2b	(+ 1.0 (cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.3b	(cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

90×	`associate-r`
80×	`times-frac`
77×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
57×	`add-cube-cbrt`
47×	`unpow-prod-down` `cube-prod`
43×	`sqrt-prod`
41×	`cbrt-prod`
24×	`add-exp-log`
12×	`prod-exp` `unswap-sqr`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def` `cbrt-unprod`
2×	`cube-div` `pow-to-exp` `associate-*r/` `div-exp` `div-inv` `sqr-pow`
1×	`+-commutative` `cube-mult` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `pow1/3` `unpow3` `associate-l` `sum-log` `*-commutative` `distribute-lft-out`

Counts

4 → 170

Calls

4 calls:

92.0ms	(* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
3.0ms	(+ 1.0 (cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
26.0ms	(cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
92.0ms	(+ 1.0 (cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
66.0ms	(cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))

simplify118.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	795	2147
1	4758	1908
2	5001	1907

prune450.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.2b

localize21.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
4.2b	(+ 1.0 (cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.3b	(cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

90×	`associate-r`
80×	`times-frac`
77×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
57×	`add-cube-cbrt`
47×	`unpow-prod-down` `cube-prod`
43×	`sqrt-prod`
41×	`cbrt-prod`
24×	`add-exp-log`
12×	`prod-exp` `unswap-sqr`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def` `cbrt-unprod`
2×	`cube-div` `pow-to-exp` `associate-*r/` `div-exp` `div-inv` `sqr-pow`
1×	`+-commutative` `cube-mult` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `pow1/3` `unpow3` `associate-l` `sum-log` `*-commutative` `distribute-lft-out`

Counts

4 → 170

Calls

4 calls:

92.0ms	(* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
3.0ms	(+ 1.0 (cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms	(cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
91.0ms	(+ 1.0 (cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
63.0ms	(cbrt (* (* x x) (pow (/ (cbrt x) (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)))

simplify119.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	795	2147
1	4758	1908
2	5001	1907

prune489.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.2b

regimes168.0ms

Accuracy

0% (0.6b remaining)

Error of 14.0b against oracle of 13.3b and baseline of 14.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	16
1	27	16

end0.0ms

sample829.0ms

Algorithm

intervals

Results

208.0ms	5975×	body	80	valid
179.0ms	823×	body	2560	valid
114.0ms	649×	body	1280	valid
110.0ms	8000×	pre	80	true
44.0ms	324×	body	640	valid
16.0ms	156×	body	320	valid
5.0ms	73×	body	160	valid