Details

sample33.0ms

Algorithm

intervals

Results

21.0ms

261×

body

valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	8
1	39	8
2	64	8
3	115	8
4	207	8
5	465	8
6	1337	8
7	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* y z) x)
0.5b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
7.3b	(/ (- (* y z) x) (- (* t z) x))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
25×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`distribute-lft-out`
7×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
5×	`add-log-exp`
4×	`associate-/r/` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `flip3--` `div-sub` `prod-diff` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`associate-+r-` `sub-neg` `fma-neg` `diff-log`

Counts

3 → 95

Calls

3 calls:

3.0ms	(- (* y z) x)
56.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
12.0ms	(/ (- (* y z) x) (- (* t z) x))

series215.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(- (* y z) x)
128.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
59.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify63.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	435	951
1	1923	872
2	5001	872

prune293.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (+ x (/ (fma y z (- x)) (- (* t z) x))) (+ x 1.0))
7.3b	(/ (fma y z (- x)) (- (* t z) x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
25×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`distribute-lft-out`
7×	`associate-/r` `associate-/l`
6×	`add-exp-log` `add-cbrt-cube`
4×	`associate-/r/`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`flip3--` `flip--`

Counts

2 → 73

Calls

2 calls:

46.0ms	(/ (+ x (/ (fma y z (- x)) (- (* t z) x))) (+ x 1.0))
6.0ms	(/ (fma y z (- x)) (- (* t z) x))

series177.0ms

Counts

2 → 6

Calls

2 calls:

113.0ms	(/ (+ x (/ (fma y z (- x)) (- (* t z) x))) (+ x 1.0))
64.0ms	(/ (fma y z (- x)) (- (* t z) x))

simplify134.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	307	828
1	1042	771
2	4468	770
3	5001	768

prune234.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (/ (- (* t z) x) (fma y z (- x))))
0.5b	(/ (+ x (/ 1 (/ (- (* t z) x) (fma y z (- x))))) (+ x 1.0))
7.1b	(/ (- (* t z) x) (fma y z (- x)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

104×	`times-frac`
91×	`*-un-lft-identity`
64×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`associate-/r*`
18×	`add-exp-log`
16×	`distribute-lft-out`
12×	`add-cbrt-cube` `div-inv`
11×	`associate-/l*`
9×	`div-exp`
5×	`cbrt-undiv`
4×	`pow1` `associate-/l/`
3×	`expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r/` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+`
1×	`flip3--` `pow-flip` `div-sub` `flip--` `inv-pow`

Counts

3 → 157

Calls

3 calls:

8.0ms	(/ 1 (/ (- (* t z) x) (fma y z (- x))))
73.0ms	(/ (+ x (/ 1 (/ (- (* t z) x) (fma y z (- x))))) (+ x 1.0))
8.0ms	(/ (- (* t z) x) (fma y z (- x)))

series309.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(/ 1 (/ (- (* t z) x) (fma y z (- x))))
145.0ms	(/ (+ x (/ 1 (/ (- (* t z) x) (fma y z (- x))))) (+ x 1.0))
65.0ms	(/ (- (* t z) x) (fma y z (- x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	554	1878
1	2508	1706
2	5002	1628

prune398.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (- (* t z) x))
0.5b	(/ (+ x (* (fma y z (- x)) (/ 1 (- (* t z) x)))) (+ x 1.0))
7.1b	(* (fma y z (- x)) (/ 1 (- (* t z) x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
32×	`times-frac`
28×	`add-cube-cbrt`
18×	`add-exp-log`
15×	`associate-r`
12×	`add-cbrt-cube`
7×	`associate-/r*`
6×	`pow1` `associate-/r/` `associate-/l*`
5×	`div-exp`
4×	`prod-exp` `distribute-lft-out`
3×	`cbrt-undiv` `expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
2×	`rec-exp` `flip3--` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip--` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 112

Calls

3 calls:

9.0ms	(/ 1 (- (* t z) x))
11.0ms	(/ (+ x (* (fma y z (- x)) (/ 1 (- (* t z) x)))) (+ x 1.0))
17.0ms	(* (fma y z (- x)) (/ 1 (- (* t z) x)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ 1 (- (* t z) x))
108.0ms	(/ (+ x (* (fma y z (- x)) (/ 1 (- (* t z) x)))) (+ x 1.0))
59.0ms	(* (fma y z (- x)) (/ 1 (- (* t z) x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	416	1082
1	1764	964
2	5001	933

prune332.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes130.0ms

Accuracy

54.8% (3.2b remaining)

Error of 3.5b against oracle of 0.3b and baseline of 7.4b

bsearch138.0ms

Steps

Iters	Range		Point
9	1.9859741489859315e+38	5.919098703954595e+44	5.844211289000958e+44
10	-4.145596723043398e-174	-4.1145167087658065e-190	-2.3616844818867944e-174

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	26
1	40	26
2	40	26

end0.0ms

sample930.0ms

Algorithm

intervals

Results

689.0ms

8351×

body

valid