Details

sample126.0ms

Algorithm

intervals

Results

46.0ms	86×	body	2560	valid
30.0ms	82×	body	1280	valid
17.0ms	258×	body	80	nan
12.0ms	43×	body	640	valid
6.0ms	26×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	6×	body	80	valid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	43	7
2	84	7
3	155	7
4	262	7
5	454	7
6	2878	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- 1.0 (* 5.0 (* v v)))
0.2b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
3.0ms	(- 1.0 (* 5.0 (* v v)))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
59.0ms	(- 1.0 (* 5.0 (* v v)))
30.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	391	750
1	1491	682
2	5002	678

prune234.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
0.0b	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.2b	(* 5.0 (* v v))
0.5b	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

435×	`add-sqr-sqrt`
389×	`times-frac`
300×	`prod-diff`
267×	`*-un-lft-identity`
199×	`add-cube-cbrt`
166×	`difference-of-squares`
84×	`associate-/r/`
43×	`flip3--` `flip--`
42×	`div-inv`
34×	`distribute-lft-out--`
33×	`unpow-prod-down` `unpow2` `sqr-pow`
30×	`fma-neg`
18×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down`
1×	`acos-asin` `sub-neg` `frac-2neg` `diff-log` `associate-r` `clear-num` `-commutative` `frac-sub` `associate-/l` `unswap-sqr`

Counts

4 → 408

Calls

4 calls:

13.0ms	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
103.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
7.0ms	(* 5.0 (* v v))
37.0ms	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series233.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
126.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
27.0ms	(* 5.0 (* v v))
5.0ms	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify193.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1248	13858
1	3989	9584
2	5001	9584

prune868.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
0.0b	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.2b	(* 5.0 (* v v))
0.5b	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

435×	`add-sqr-sqrt`
389×	`times-frac`
300×	`prod-diff`
267×	`*-un-lft-identity`
199×	`add-cube-cbrt`
166×	`difference-of-squares`
84×	`associate-/r/`
43×	`flip3--` `flip--`
42×	`div-inv`
34×	`distribute-lft-out--`
33×	`unpow-prod-down` `unpow2` `sqr-pow`
30×	`fma-neg`
18×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down`
1×	`sub-neg` `asin-acos` `frac-2neg` `diff-log` `associate-r` `clear-num` `-commutative` `frac-sub` `associate-/l` `unswap-sqr`

Counts

4 → 408

Calls

4 calls:

12.0ms	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
104.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
6.0ms	(* 5.0 (* v v))
23.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series233.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
121.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
26.0ms	(* 5.0 (* v v))
12.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify194.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1248	13858
1	3989	9584
2	5001	9584

prune945.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

0.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
7.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
18.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
21.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
4.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify115.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	132	1070
1	439	956
2	2385	912
3	5002	881

prune168.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes122.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	12
1	17	12

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	2999×	body	2560	valid
934.0ms	2538×	body	1280	valid
536.0ms	8033×	body	80	nan
344.0ms	1224×	body	640	valid
130.0ms	617×	body	320	valid
64.0ms	414×	body	160	valid
24.0ms	208×	body	80	valid