Details

sample35.0ms

Algorithm

intervals

Results

15.0ms	363×	body	80	valid
5.0ms	141×	body	80	nan

simplify109.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma k 10.0 1.0)
0.1b	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
0.3b	(fma k k (fma k 10.0 1.0))
3.3b	(/ (fma k k (fma k 10.0 1.0)) a)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
96×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`unpow-prod-down`
19×	`add-exp-log`
16×	`associate-/r*`
14×	`sqr-pow`
11×	`add-cbrt-cube`
10×	`div-exp` `div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `fma-udef`
1×	`associate-/r/`

Counts

4 → 181

Calls

4 calls:

0.0ms	(fma k 10.0 1.0)
7.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
0.0ms	(fma k k (fma k 10.0 1.0))
2.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

series221.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(fma k 10.0 1.0)
114.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
23.0ms	(fma k k (fma k 10.0 1.0))
53.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

simplify93.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	715	1922
1	3280	1854
2	5002	1852

prune581.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma k 10.0 1.0)
0.1b	(/ (pow k m) (fma k k (fma k 10.0 1.0)))
0.3b	(fma k k (fma k 10.0 1.0))
1.9b	(* (/ (pow k m) (fma k k (fma k 10.0 1.0))) a)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-l`
22×	`unpow-prod-down`
19×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`sqr-pow`
7×	`associate-/l*`
6×	`pow1` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r` `associate-/r*`
2×	`cbrt-undiv` `pow-to-exp` `pow-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 117

Calls

4 calls:

0.0ms	(fma k 10.0 1.0)
4.0ms	(/ (pow k m) (fma k k (fma k 10.0 1.0)))
0.0ms	(fma k k (fma k 10.0 1.0))
13.0ms	(* (/ (pow k m) (fma k k (fma k 10.0 1.0))) a)

series248.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma k 10.0 1.0)
77.0ms	(/ (pow k m) (fma k k (fma k 10.0 1.0)))
23.0ms	(fma k k (fma k 10.0 1.0))
111.0ms	(* (/ (pow k m) (fma k k (fma k 10.0 1.0))) a)

simplify53.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	488	962
1	1842	899
2	5001	887

prune387.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow k m) (fma k k (fma k 10.0 1.0)))
0.3b	(fma k k (fma k 10.0 1.0))
1.9b	(* (cbrt (pow (/ (pow k m) (fma k k (fma k 10.0 1.0))) 3)) a)
4.1b	(cbrt (pow (/ (pow k m) (fma k k (fma k 10.0 1.0))) 3))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

122×	`cbrt-prod`
111×	`times-frac`
105×	`add-sqr-sqrt`
104×	`unpow-prod-down`
80×	`add-cube-cbrt` `*-un-lft-identity`
59×	`associate-l`
54×	`cube-prod`
21×	`sqr-pow`
11×	`add-exp-log` `unswap-sqr`
7×	`add-cbrt-cube` `associate-/l*`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`cube-div` `cube-mult` `cbrt-div` `unpow3`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow1/3` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `-commutative` `rem-cbrt-cube` `cbrt-unprod` `fma-udef`

Counts

4 → 212

Calls

4 calls:

4.0ms	(/ (pow k m) (fma k k (fma k 10.0 1.0)))
0.0ms	(fma k k (fma k 10.0 1.0))
41.0ms	(* (cbrt (pow (/ (pow k m) (fma k k (fma k 10.0 1.0))) 3)) a)
12.0ms	(cbrt (pow (/ (pow k m) (fma k k (fma k 10.0 1.0))) 3))

series280.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (pow k m) (fma k k (fma k 10.0 1.0)))
29.0ms	(fma k k (fma k 10.0 1.0))
110.0ms	(* (cbrt (pow (/ (pow k m) (fma k k (fma k 10.0 1.0))) 3)) a)
71.0ms	(cbrt (pow (/ (pow k m) (fma k k (fma k 10.0 1.0))) 3))

simplify100.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	800	1952
1	3470	1912
2	5001	1906

prune600.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
6.3b	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
6.3b	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
11.7b	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
19×	`times-frac` `associate-/r*`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`unpow-prod-down` `div-exp`
8×	`exp-neg` `distribute-rgt-neg-out` `associate-/l/`
6×	`cube-prod` `associate-*r/` `prod-exp` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `mul-1-neg` `log-rec` `pow-exp` `un-div-inv` `log1p-expm1-u` `sqr-pow`
2×	`cube-mult` `frac-2neg` `unpow3` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `frac-sub` `flip--` `fma-udef`

Counts

4 → 115

Calls

4 calls:

0.0ms	(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
19.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
19.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
51.0ms	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

series705.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
81.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
78.0ms	(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
366.0ms	(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

simplify103.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	623	1864
1	3171	1567
2	5001	1493

prune564.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes87.0ms

Accuracy

98.6% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.1b

bsearch51.0ms

Steps

Iters	Range		Point
7	2.4240874598562344e+151	2.2744812316711812e+153	1.4321778772581635e+152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	32
1	49	32
2	49	32

end0.0ms

sample961.0ms

Algorithm

intervals

Results

473.0ms	11892×	body	80	valid
144.0ms	4212×	body	80	nan