Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify129.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (6.0ms)

Iter	Nodes	Cost
0	31	9
1	59	9
2	90	9
3	116	7
4	130	7
5	148	7
6	188	7
7	264	7
8	304	7
9	377	7
10	580	7
11	851	7
12	1402	7
13	2787	7
14	3168	7
15	4321	7
16	5001	7

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- x) 0.70711 (/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0)))
0.0b	(fma x (fma 0.04481 x 0.99229) 1.0)
0.1b	(* 0.70711 (fma 0.27061 x 2.30753))
17.1b	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

0.0ms	(fma (- x) 0.70711 (/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0)))
0.0ms	(fma x (fma 0.04481 x 0.99229) 1.0)
3.0ms	(* 0.70711 (fma 0.27061 x 2.30753))
4.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0))

series232.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma (- x) 0.70711 (/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0)))
31.0ms	(fma x (fma 0.04481 x 0.99229) 1.0)
49.0ms	(* 0.70711 (fma 0.27061 x 2.30753))
77.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (fma x (fma 0.04481 x 0.99229) 1.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	272	452
1	1121	382
2	5002	382

prune215.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)
0.1b	(* 0.70711 (fma 0.27061 x 2.30753))
9.3b	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
17.1b	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac` `associate-/r*`
12×	`add-exp-log` `unpow-prod-down` `cube-prod`
10×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef`
1×	`distribute-rgt-in` `pow-to-exp` `pow-pow` `frac-2neg` `distribute-lft-in` `pow1/3` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `rem-cbrt-cube` `div-inv` `associate-/l` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

1.0ms	(pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)
3.0ms	(* 0.70711 (fma 0.27061 x 2.30753))
1.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
7.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)
52.0ms	(* 0.70711 (fma 0.27061 x 2.30753))
32.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
78.0ms	(/ (* 0.70711 (fma 0.27061 x 2.30753)) (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))

simplify60.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	392	766
1	1802	690
2	5001	675

prune345.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753))) (sqrt (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
9.3b	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
17.1b	(sqrt (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))
17.1b	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

3558×	`times-frac`
1611×	`sqrt-prod`
1555×	`add-sqr-sqrt`
1550×	`add-cube-cbrt` `*-un-lft-identity`
892×	`cbrt-prod`
223×	`unpow-prod-down` `cube-prod`
77×	`div-inv`
75×	`sqr-pow`
74×	`cube-mult` `unpow3`
71×	`associate-/l*`
19×	`associate-/r/`
18×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-undiv` `rem-sqrt-square` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1`
2×	`pow1/2` `pow1/3`
1×	`frac-2neg` `clear-num` `rem-cbrt-cube` `associate-/l/`

Counts

4 → 1456

Calls

4 calls:

47.0ms	(/ (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753))) (sqrt (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
1.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
7.0ms	(sqrt (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))
1.0ms	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))

series332.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753))) (sqrt (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))))
33.0ms	(cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3))
103.0ms	(sqrt (cbrt (pow (fma x (fma 0.04481 x 0.99229) 1.0) 3)))
102.0ms	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))

simplify418.0ms

Algorithm

egg-herbie

Counts

1468 → 1468

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	3956	37626
1	5002	35261

prune3.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

17.1b	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))
17.1b	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))
17.1b	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))
20.9b	(cbrt (* (/ (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753))) (fma x (fma 0.04481 x 0.99229) 1.0)) (/ (* (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753))) (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753)))) (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2`
1×	`cbrt-prod` `frac-times` `pow1/3` `associate-r/` `associate-l/`

Counts

4 → 59

Calls

4 calls:

1.0ms	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))
1.0ms	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))
1.0ms	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))
75.0ms	(cbrt (* (/ (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753))) (fma x (fma 0.04481 x 0.99229) 1.0)) (/ (* (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753))) (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753)))) (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))
89.0ms	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))
90.0ms	(sqrt (fma x (fma 0.04481 x 0.99229) 1.0))
117.0ms	(cbrt (* (/ (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753))) (fma x (fma 0.04481 x 0.99229) 1.0)) (/ (* (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753))) (/ 0.70711 (/ (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)) (fma 0.27061 x 2.30753)))) (sqrt (fma x (fma 0.04481 x 0.99229) 1.0)))))

simplify98.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	241	824
1	763	739
2	3591	687
3	5001	670

prune334.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	30
1	21	30

end0.0ms

sample358.0ms

Algorithm

intervals

Results

265.0ms

8000×

body

valid