Details

sample114.0ms

Algorithm

intervals

Results

47.0ms	100×	body	2560	valid
22.0ms	68×	body	1280	valid
15.0ms	280×	body	80	nan
11.0ms	46×	body	640	valid
3.0ms	16×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	10×	body	80	valid

simplify94.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* 5.0 (* v v)))
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)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp`
4×	`associate-/r*` `difference-of-squares`
3×	`flip3--` `associate-l` `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 → 75

Calls

4 calls:

2.0ms	(- 1.0 (* 5.0 (* v v)))
9.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- 1.0 (* 5.0 (* v v)))
82.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	355	664
1	1356	609
2	5001	605

prune192.0ms

Pruning

4 alts after pruning (4 fresh and 0 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 (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))

rewrite22.0ms

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))
2.0ms	(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 5.0 (* v v))
24.0ms	(* 5.0 (* v v))
29.0ms	(* 5.0 (* v v))
10.0ms	(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	174	461
1	607	394
2	2607	394
3	5001	394

prune192.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize19.0ms

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 (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))

rewrite26.0ms

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:

7.0ms	(* 5.0 (* v v))
6.0ms	(* 5.0 (* v v))
10.0ms	(* 5.0 (* v v))
2.0ms	(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* 5.0 (* v v))
24.0ms	(* 5.0 (* v v))
24.0ms	(* 5.0 (* v v))
10.0ms	(acos (/ (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0))) (- (* v v) 1.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	174	461
1	607	394
2	2607	394
3	5001	394

prune226.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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:

11.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series147.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
83.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms	(* 5.0 (* v v))
4.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (34.0ms)

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

prune221.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes66.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	20
1	23	20

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	3064×	body	2560	valid
799.0ms	2456×	body	1280	valid
436.0ms	7965×	body	80	nan
301.0ms	1226×	body	640	valid
114.0ms	625×	body	320	valid
52.0ms	401×	body	160	valid
17.0ms	228×	body	80	valid