Details

sample82.0ms

Algorithm

intervals

Results

33.0ms	95×	body	2560	valid
19.0ms	87×	body	1280	valid
10.0ms	242×	body	80	nan
7.0ms	45×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	8×	body	80	valid

simplify99.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series118.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	336	587
1	1261	535
2	5002	531

prune158.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b	(* 5.0 (* v v))
0.6b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
30.0ms	(* 5.0 (* v v))
3.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	409	840
1	1459	784
2	5001	780

prune234.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow v 2) (pow v 4))
0.0b	(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.7b	(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`associate-r`
3×	`associate-l`
2×	`asin-acos` `flip3-+` `associate-*r/` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `times-frac` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

7.0ms	(+ (pow v 2) (pow v 4))
7.0ms	(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
10.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms	(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series213.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (pow v 2) (pow v 4))
38.0ms	(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
95.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms	(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify209.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	250	546
1	1032	503
2	4958	497
3	5001	497

prune180.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.6b	(acos (* (/ (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (+ v (sqrt 1.0))) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`associate-r` `*-commutative` `unswap-sqr`
1×	`acos-asin`

Counts

4 → 65

Calls

4 calls:

6.0ms	(* 5.0 (* v v))
6.0ms	(* 5.0 (* v v))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (/ (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (+ v (sqrt 1.0))) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0)))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 5.0 (* v v))
25.0ms	(* 5.0 (* v v))
30.0ms	(* 5.0 (* v v))
12.0ms	(acos (* (/ (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (+ v (sqrt 1.0))) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (- v (sqrt 1.0)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	149	498
1	500	410
2	1475	410
3	5001	410

prune196.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes66.0ms

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	14	9
1	14	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2999×	body	2560	valid
588.0ms	2518×	body	1280	valid
222.0ms	7917×	body	80	nan
200.0ms	1219×	body	640	valid
75.0ms	632×	body	320	valid
34.0ms	415×	body	160	valid
10.0ms	217×	body	80	valid