Details

sample81.0ms

Algorithm

intervals

Results

34.0ms	98×	body	2560	valid
17.0ms	78×	body	1280	valid
7.0ms	272×	body	80	nan
7.0ms	41×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	4×	body	80	valid

simplify99.0ms

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 3 expressions with local error:

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

rewrite19.0ms

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:

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)))

series117.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
26.0ms	(* 5.0 (* v v))
8.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify38.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (30.0ms)

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

prune176.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `associate-r` `*-commutative` `unswap-sqr`
1×	`acos-asin` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 69

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (* 5.0 (* v v))))
6.0ms	(* 5.0 (* v v))
7.0ms	(* 5.0 (* v v))
0.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (- 1.0 (* 5.0 (* v v))))
29.0ms	(* 5.0 (* v v))
24.0ms	(* 5.0 (* v v))
4.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

simplify114.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	264	505
1	875	452
2	4161	451
3	5002	451

prune205.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 1 expressions with local error:

0.5b	(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:

0.0ms

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

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

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

simplify93.0ms

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

prune40.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
0.0b	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
0.5b	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 32

Calls

3 calls:

0.0ms	(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
0.0ms	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
0.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series276.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
164.0ms	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
6.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify95.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	56	296
1	88	258
2	187	256
3	462	256
4	1961	256
5	5001	256

prune103.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

regimes53.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	13
1	13	13

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2937×	body	2560	valid
597.0ms	2545×	body	1280	valid
231.0ms	8079×	body	80	nan
208.0ms	1240×	body	640	valid
78.0ms	648×	body	320	valid
35.0ms	414×	body	160	valid
11.0ms	216×	body	80	valid