Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	33×	body	2560	valid
7.0ms	198×	body	80	valid
4.0ms	256×	pre	80	true
2.0ms	12×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 11.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
18.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* 4.0 p) p) (* x x))
56.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify152.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (142.0ms)

Iter	Nodes	Cost
0	296	867
1	1081	815
2	4584	798
3	5001	795

prune305.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.5b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
18.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `add-log-exp`
8×	`exp-prod`
6×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod` `distribute-lft-out`
2×	`flip3-+` `sqrt-div` `exp-sum` `sum-log` `flip-+` `rem-exp-log`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp`

Counts

4 → 69

Calls

4 calls:

13.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
71.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify114.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	219	629
1	680	567
2	1814	566
3	4609	565
4	5001	565

prune293.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(expm1 (log1p (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b	(log (expm1 (log1p (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
18.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`pow1` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod` `fma-def` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `distribute-lft-out` `expm1-udef`

Counts

4 → 59

Calls

4 calls:

1.0ms	(expm1 (log1p (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.0ms	(log (expm1 (log1p (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series910.0ms

Counts

4 → 12

Calls

4 calls:

362.0ms	(expm1 (log1p (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
413.0ms	(log (expm1 (log1p (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify113.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	209	657
1	593	531
2	1763	530
3	4868	521
4	5001	521

prune296.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.6b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
18.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`pow-flip` `fma-def` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 133

Calls

4 calls:

8.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
52.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	384	1256
1	1710	1134
2	5001	1063

prune331.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.1b

regimes156.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	13
1	23	13

end0.0ms

sample858.0ms

Algorithm

intervals

Results

226.0ms	6045×	body	80	valid
179.0ms	775×	body	2560	valid
115.0ms	617×	body	1280	valid
109.0ms	8000×	pre	80	true
45.0ms	317×	body	640	valid
17.0ms	157×	body	320	valid
6.0ms	89×	body	160	valid