Details

sample78.0ms

Algorithm

intervals

Results

35.0ms	108×	body	2560	valid
15.0ms	72×	body	1280	valid
7.0ms	270×	body	80	nan
6.0ms	40×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	12×	body	80	valid

simplify97.0ms

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

localize7.0ms

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))
0.1b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite21.0ms

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:

2.0ms	(- 1.0 (* 5.0 (* v v)))
10.0ms	(/ (- 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)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- 1.0 (* 5.0 (* v v)))
89.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
7.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (36.0ms)

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

prune233.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.1b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

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`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `expm1-log1p` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0ms	(expm1 (log1p (acos (/ (- 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)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
139.0ms	(expm1 (log1p (acos (/ (- 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

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	361	749
1	1295	678
2	5001	676

prune244.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.0b	(expm1 (log1p (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))
0.1b	(* 5.0 (* v v))
0.6b	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

431×	`add-sqr-sqrt`
385×	`times-frac`
300×	`prod-diff`
265×	`*-un-lft-identity`
197×	`add-cube-cbrt`
164×	`difference-of-squares`
82×	`associate-/r/`
42×	`flip3--` `flip--`
41×	`div-inv`
34×	`distribute-lft-out--`
33×	`unpow-prod-down` `unpow2` `sqr-pow`
30×	`fma-neg`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`acos-asin` `sub-neg` `expm1-log1p` `diff-log` `associate-r` `*-commutative` `frac-sub` `expm1-udef` `unswap-sqr`

Counts

4 → 390

Calls

4 calls:

100.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.0ms	(expm1 (log1p (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))
6.0ms	(* 5.0 (* v v))
33.0ms	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
146.0ms	(expm1 (log1p (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))
34.0ms	(* 5.0 (* v v))
5.0ms	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify174.0ms

Algorithm

egg-herbie

Counts

402 → 402

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1151	13922
1	3354	9532
2	5002	9529

prune968.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.0b	(expm1 (log1p (- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))))
0.1b	(* 5.0 (* v v))
0.7b	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

431×	`add-sqr-sqrt`
385×	`times-frac`
300×	`prod-diff`
265×	`*-un-lft-identity`
197×	`add-cube-cbrt`
164×	`difference-of-squares`
82×	`associate-/r/`
42×	`flip3--` `flip--`
41×	`div-inv`
34×	`distribute-lft-out--`
33×	`unpow-prod-down` `unpow2` `sqr-pow`
30×	`fma-neg`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`sub-neg` `asin-acos` `expm1-log1p` `diff-log` `associate-r` `*-commutative` `frac-sub` `expm1-udef` `unswap-sqr`

Counts

4 → 390

Calls

4 calls:

98.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.0ms	(expm1 (log1p (- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))))
6.0ms	(* 5.0 (* v v))
22.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
275.0ms	(expm1 (log1p (- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))))
35.0ms	(* 5.0 (* v v))
5.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify182.0ms

Algorithm

egg-herbie

Counts

402 → 402

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1162	13854
1	3311	9578
2	5001	9571

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes75.0ms

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	12	9
1	12	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	2978×	body	2560	valid
552.0ms	2475×	body	1280	valid
218.0ms	8063×	body	80	nan
199.0ms	1259×	body	640	valid
74.0ms	647×	body	320	valid
33.0ms	408×	body	160	valid
11.0ms	233×	body	80	valid