Details

sample25.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 3.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1.1283791670955126 (exp z))
1.4b	(- (* 1.1283791670955126 (exp z)) (* x y))
8.3b	(/ y (- (* 1.1283791670955126 (exp z)) (* x y)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

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

series151.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(* 1.1283791670955126 (exp z))
60.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
74.0ms	(/ y (- (* 1.1283791670955126 (exp z)) (* x y)))

simplify36.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	290	501
1	1077	461
2	5001	459

prune195.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1.1283791670955126 (exp z))
0.7b	(/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))
1.4b	(- (* 1.1283791670955126 (exp z)) (* x y))
7.8b	(* y (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`times-frac`
18×	`add-exp-log` `associate-r`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`flip3--` `associate-/r` `flip--` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 111

Calls

4 calls:

5.0ms	(* 1.1283791670955126 (exp z))
9.0ms	(/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))
4.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
22.0ms	(* y (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y))))

series202.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* 1.1283791670955126 (exp z))
61.0ms	(/ 1 (- (* 1.1283791670955126 (exp z)) (* x y)))
58.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
66.0ms	(* y (/ 1 (- (* 1.1283791670955126 (exp z)) (* x y))))

simplify59.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	429	868
1	1928	771
2	5002	740

prune278.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
1.4b	(- (* 1.1283791670955126 (exp z)) (* x y))
3.2b	(/ (cbrt y) (- (* 1.1283791670955126 (exp z)) (* x y)))
5.2b	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (- (* 1.1283791670955126 (exp z)) (* x y))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `times-frac`
33×	`add-cube-cbrt` `*-un-lft-identity`
25×	`cbrt-prod`
24×	`associate-r`
18×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `associate-/r*` `flip--` `unswap-sqr`
2×	`div-inv`
1×	`sub-neg` `frac-2neg` `fma-neg` `pow1/3` `diff-log` `associate-r/` `associate-l` `prod-diff` `clear-num` `-commutative`

Counts

4 → 121

Calls

4 calls:

0.0ms	(cbrt y)
4.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
9.0ms	(/ (cbrt y) (- (* 1.1283791670955126 (exp z)) (* x y)))
33.0ms	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (- (* 1.1283791670955126 (exp z)) (* x y))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt y)
54.0ms	(- (* 1.1283791670955126 (exp z)) (* x y))
222.0ms	(/ (cbrt y) (- (* 1.1283791670955126 (exp z)) (* x y)))
93.0ms	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (- (* 1.1283791670955126 (exp z)) (* x y))))

simplify77.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	591	1363
1	2816	1189
2	5002	1146

prune446.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.2b

localize16.0ms

Local error

Found 4 expressions with local error:

8.3b	(/ y (* (* (cbrt (- (* 1.1283791670955126 (exp z)) (* x y))) (cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))) (cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))))
8.8b	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))
8.8b	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))
8.8b	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`associate-/r/`
14×	`associate-*l/`
13×	`add-exp-log`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`associate-*r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `pow1/3` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 96

Calls

4 calls:

50.0ms	(/ y (* (* (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)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ y (* (* (cbrt (- (* 1.1283791670955126 (exp z)) (* x y))) (cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))) (cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))))
120.0ms	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))
116.0ms	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))
119.0ms	(cbrt (- (* 1.1283791670955126 (exp z)) (* x y)))

simplify96.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	454	1769
1	1241	1600
2	4515	1453
3	5001	1426

prune369.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 1.2b

regimes202.0ms

Accuracy

77.1% (0.2b remaining)

Error of 1.9b against oracle of 1.7b and baseline of 2.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

end0.0ms

sample818.0ms

Algorithm

intervals

Results

644.0ms

8002×

body

valid