Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	6
1	24	6
2	28	6
3	28	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1.1283791670955126 (exp z))
0.0b	(+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))
0.6b	(- (* 1.1283791670955126 (exp z)) (* x y))
7.6b	(/ y (- (* 1.1283791670955126 (exp z)) (* x y)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-log-exp`
7×	`add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-exp` `prod-diff` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

5.0ms	(* 1.1283791670955126 (exp z))
17.0ms	(+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))
4.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
8.0ms	(/ y (- (* 1.1283791670955126 (exp z)) (* x y)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* 1.1283791670955126 (exp z))
34.0ms	(+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))
57.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
70.0ms	(/ y (- (* 1.1283791670955126 (exp z)) (* x y)))

simplify45.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	356	637
1	1280	593
2	5001	590

prune244.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))))
0.5b	(/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))
0.6b	(- (* 1.1283791670955126 (exp z)) (* x y))
7.1b	(* y (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `fma-def` `associate-l` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 107

Calls

4 calls:

2.0ms	(+ x (* y (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))))
9.0ms	(/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))
4.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
24.0ms	(* y (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ x (* y (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))))
58.0ms	(/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))
54.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
70.0ms	(* y (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y))))

simplify63.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	451	942
1	1976	841
2	5001	805

prune272.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

7.1b	(* y (/ (/ 1 (* (cbrt (- (* 1.1283791670955126 (exp z)) (* x y))) (cbrt (- (* 1.1283791670955126 (exp z)) (* x y))))) (cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))))
8.0b	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))
8.0b	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))
8.0b	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
96×	`associate-r`
80×	`cbrt-div`
69×	`add-sqr-sqrt`
57×	`cbrt-prod`
53×	`*-un-lft-identity`
51×	`add-cube-cbrt`
50×	`associate-/r/`
40×	`flip3--` `flip--`
32×	`add-exp-log`
24×	`frac-times`
13×	`associate-*r/` `add-cbrt-cube`
12×	`associate-*l/`
11×	`div-exp` `prod-exp`
7×	`div-inv` `unswap-sqr`
6×	`pow1`
5×	`cbrt-undiv` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l`
2×	`rec-exp` `1-exp`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 175

Calls

4 calls:

115.0ms	(* y (/ (/ 1 (* (cbrt (- (* 1.1283791670955126 (exp z)) (* x y))) (cbrt (- (* 1.1283791670955126 (exp z)) (* x y))))) (cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))))
4.0ms	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))
4.0ms	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))
4.0ms	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* y (/ (/ 1 (* (cbrt (- (* 1.1283791670955126 (exp z)) (* x y))) (cbrt (- (* 1.1283791670955126 (exp z)) (* x y))))) (cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))))
113.0ms	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))
112.0ms	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))
113.0ms	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))

simplify125.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	1000	3462
1	4481	3110
2	5001	3071

prune673.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (log1p (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))))
0.5b	(/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))
0.6b	(- (* 1.1283791670955126 (exp z)) (* x y))
6.2b	(* y (expm1 (log1p (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`flip3--` `div-exp` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `expm1-log1p` `pow-flip` `frac-2neg` `fma-neg` `diff-log` `1-exp` `prod-diff` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow` `expm1-udef` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

0.0ms	(expm1 (log1p (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))))
9.0ms	(/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))
4.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
3.0ms	(* y (expm1 (log1p (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y))))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(expm1 (log1p (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))))
58.0ms	(/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))
54.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
125.0ms	(* y (expm1 (log1p (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	337	758
1	1410	656
2	5001	635

prune241.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes103.0ms

Accuracy

59.3% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 2.9b

bsearch1.0ms

Steps

Iters	Range		Point
0	0.9992773459915872	0.9998754085065553	0.9995763772490712

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	10
1	23	10

end0.0ms

sample416.0ms

Algorithm

intervals

Results

246.0ms

8000×

body

valid