Details

sample80.0ms

Algorithm

intervals

Results

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

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 0.6b

localize12.0ms

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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 69

Calls

3 calls:

8.0ms	(/ (- 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)))

series114.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(/ (- 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)))

simplify42.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	349	623
1	1288	567
2	5001	565

prune189.0ms

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)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`add-cube-cbrt`
49×	`times-frac`
39×	`prod-diff`
13×	`fma-neg`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp` `difference-of-squares`
5×	`div-inv`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
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` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 139

Calls

4 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
9.0ms	(- (/ PI 2) (asin (/ (- 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)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
31.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
32.0ms	(* 5.0 (* v v))
4.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	576	2948
1	1941	1851
2	5003	1839

prune327.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 1 expressions with local error:

0.6b	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `acos-asin` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series7.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify97.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	30	93
1	54	82
2	153	82
3	423	82
4	1909	82
5	5001	82

prune42.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize22.0ms

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	(asin (* (/ (* (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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `*-commutative` `unswap-sqr`
1×	`asin-acos`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* 5.0 (* v v))
6.0ms	(* 5.0 (* v v))
6.0ms	(* 5.0 (* v v))
1.0ms	(asin (* (/ (* (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)))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 5.0 (* v v))
31.0ms	(* 5.0 (* v v))
25.0ms	(* 5.0 (* v v))
13.0ms	(asin (* (/ (* (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)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	153	560
1	505	472
2	1506	472
3	5001	472

prune253.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

regimes87.0ms

Accuracy

0% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	25
1	25	25

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2999×	body	2560	valid
588.0ms	2518×	body	1280	valid
228.0ms	7917×	body	80	nan
205.0ms	1219×	body	640	valid
76.0ms	632×	body	320	valid
35.0ms	415×	body	160	valid
11.0ms	217×	body	80	valid