Details

sample78.0ms

Algorithm

intervals

Results

30.0ms	89×	body	2560	valid
18.0ms	82×	body	1280	valid
8.0ms	273×	body	80	nan
7.0ms	45×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	7×	body	80	valid

simplify99.0ms

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: 0.7b

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))
0.7b	(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)))

series113.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (31.0ms)

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

prune180.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize8.0ms

Local error

Found 1 expressions with local error:

0.7b	(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)))

series7.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

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

simplify94.0ms

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

prune43.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
0.0b	(exp (log (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
0.7b	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `exp-prod`
3×	`expm1-log1p-u` `exp-sum` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-pow`
1×	`acos-asin` `rem-log-exp` `rem-exp-log`

Counts

3 → 41

Calls

3 calls:

1.0ms	(log (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
1.0ms	(exp (log (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)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(log (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
7.0ms	(exp (log (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)))

simplify168.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	70	388
1	116	346
2	246	334
3	702	328
4	4008	328
5	5001	328

prune134.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))
1.0b	(pow (cbrt (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))) 2)
1.0b	(cbrt (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
1.0b	(cbrt (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`pow-pow`
1×	`acos-asin` `pow-to-exp` `pow-exp` `unpow2` `sqr-pow`

Counts

4 → 60

Calls

4 calls:

0.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))
2.0ms	(pow (cbrt (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))) 2)
0.0ms	(cbrt (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
1.0ms	(cbrt (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))

series695.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))
195.0ms	(pow (cbrt (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))) 2)
156.0ms	(cbrt (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
338.0ms	(cbrt (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))

simplify67.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	128	586
1	392	530
2	1784	517
3	5001	514

prune216.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

regimes31.0ms

Accuracy

0% (0.0b remaining)

Error of 0.7b against oracle of 0.7b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

979.0ms	2911×	body	2560	valid
571.0ms	2578×	body	1280	valid
221.0ms	8140×	body	80	nan
201.0ms	1259×	body	640	valid
72.0ms	624×	body	320	valid
37.0ms	422×	body	160	valid
10.0ms	206×	body	80	valid